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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_e829a82e-c5c2-4beb-bcf3-455769e1101e_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Issued Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets_8b541d61-2ab8-4ea8-83d0-ae2d42f24a34_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Loans in pool</link:label>
    <link:label id="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets_label_en-US" xlink:label="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral, Number Of Mortgage Assets</link:label>
    <link:label id="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral, Number of Mortgage Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:href="bsprt-20250930.xsd#bsprt_DebtInstrumentCollateralNumberOfMortgageAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:to="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_cec56939-9180-49ff-a139-9d599484e03b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Costs Incurred From Arrangements with Advisor and Affiliates</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FixedRateMember_fbdca247-45c8-49d9-a4df-b7e85769274d_terseLabel_en-US" xlink:label="lab_bsprt_FixedRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Rate</link:label>
    <link:label id="lab_bsprt_FixedRateMember_label_en-US" xlink:label="lab_bsprt_FixedRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Rate [Member]</link:label>
    <link:label id="lab_bsprt_FixedRateMember_documentation_en-US" xlink:label="lab_bsprt_FixedRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FixedRateMember" xlink:href="bsprt-20250930.xsd#bsprt_FixedRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FixedRateMember" xlink:to="lab_bsprt_FixedRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_2372d832-d886-4a74-ad7e-6c0e3bd431a7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Not Carried at Fair Value</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillLineItems_57ba9db2-0e62-4533-a207-83b92554179a_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillLineItems" xlink:to="lab_us-gaap_GoodwillLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_2aa07cf5-21bb-44c7-806c-255a80f1a832_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_24428d30-2480-4dd2-9265-ddc859ca65ae_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions and Arrangements</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_a24337b6-d11c-4f76-be9e-84ac230791fc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_240227b4-f03a-4795-9252-179b7c18c423_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of repurchase agreements and revolving credit facilities - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_label_en-US" xlink:label="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments From Securities Purchased Under Agreements To Resell, Loans Receivable</link:label>
    <link:label id="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_documentation_en-US" xlink:label="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments From Securities Purchased Under Agreements To Resell, Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:href="bsprt-20250930.xsd#bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:to="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_fefcfbff-4115-4377-9c53-9c3b46d51b14_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure_6365dbe2-4136-46b6-8e20-f2e3ca9ec1ff_terseLabel_en-US" xlink:label="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain/(loss) on sale of commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure_label_en-US" xlink:label="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Sale Of Mortgage Loans, Fair Value Disclosure</link:label>
    <link:label id="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure_documentation_en-US" xlink:label="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Sale Of Mortgage Loans, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:href="bsprt-20250930.xsd#bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:to="lab_bsprt_GainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FairValueInputsDiscountRate_f26478f1-40d0-4025-8c45-8050f762a609_terseLabel_en-US" xlink:label="lab_bsprt_FairValueInputsDiscountRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate (percentage)</link:label>
    <link:label id="lab_bsprt_FairValueInputsDiscountRate_label_en-US" xlink:label="lab_bsprt_FairValueInputsDiscountRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Discount Rate</link:label>
    <link:label id="lab_bsprt_FairValueInputsDiscountRate_documentation_en-US" xlink:label="lab_bsprt_FairValueInputsDiscountRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FairValueInputsDiscountRate" xlink:href="bsprt-20250930.xsd#bsprt_FairValueInputsDiscountRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FairValueInputsDiscountRate" xlink:to="lab_bsprt_FairValueInputsDiscountRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DilutedNumeratorAbstract_11a672bd-07fa-4187-9087-da6cb303ae49_terseLabel_en-US" xlink:label="lab_bsprt_DilutedNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted Numerator [Abstract]</link:label>
    <link:label id="lab_bsprt_DilutedNumeratorAbstract_label_en-US" xlink:label="lab_bsprt_DilutedNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diluted Numerator [Abstract]</link:label>
    <link:label id="lab_bsprt_DilutedNumeratorAbstract_documentation_en-US" xlink:label="lab_bsprt_DilutedNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diluted Numerator</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DilutedNumeratorAbstract" xlink:href="bsprt-20250930.xsd#bsprt_DilutedNumeratorAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DilutedNumeratorAbstract" xlink:to="lab_bsprt_DilutedNumeratorAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward_c8e15969-14ac-4a6c-a8d8-044982dfbc69_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_9f28407d-1da0-4516-a186-555b505df617_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_2878f156-d1ce-44aa-b950-5172c222327e_verboseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">% of Portfolio</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_8628f77d-01f9-46e8-b717-64b23dfa5e80_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour_9c337764-be6d-4b7c-9168-8f3e029fc9b8_terseLabel_en-US" xlink:label="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and beyond</link:label>
    <link:label id="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour_label_en-US" xlink:label="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, After Year Four</link:label>
    <link:label id="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:href="bsprt-20250930.xsd#bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:to="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_da4917b8-7682-4359-8313-654f7987e9f4_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnsecuredJuniorDebtMember_43aa5ca3-1ebd-47fd-a1cb-2ec4a1a9120f_terseLabel_en-US" xlink:label="lab_bsprt_UnsecuredJuniorDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt</link:label>
    <link:label id="lab_bsprt_UnsecuredJuniorDebtMember_label_en-US" xlink:label="lab_bsprt_UnsecuredJuniorDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Junior Debt [Member]</link:label>
    <link:label id="lab_bsprt_UnsecuredJuniorDebtMember_documentation_en-US" xlink:label="lab_bsprt_UnsecuredJuniorDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Junior Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnsecuredJuniorDebtMember" xlink:href="bsprt-20250930.xsd#bsprt_UnsecuredJuniorDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_UnsecuredJuniorDebtMember" xlink:to="lab_bsprt_UnsecuredJuniorDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_35108d9d-8bf2-4ce2-8e06-f60d5b25b6d4_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_da906932-c16b-493a-a76e-186f7065147c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash payments for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaid" xlink:to="lab_us-gaap_IncomeTaxesPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_72b8a0ef-0f2b-4da2-83fb-7b80f7add499_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_572b1a8b-dadd-4c88-ae60-90b602764c8c_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_58fa522e-f21e-4028-9e7c-5045e71bd27f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_1210feb8-349f-404c-b1dd-c66d1db08a93_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NY_f2698ea3-3f6c-4d69-93d6-a2762eb32e33_terseLabel_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York</link:label>
    <link:label id="lab_stpr_NY_label_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NEW YORK</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NY" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_NY"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_NY" xlink:to="lab_stpr_NY" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanMortgageHeldForSale_b5ed93d9-e712-4219-a1d4-b65e13496d4d_terseLabel_en-US" xlink:label="lab_bsprt_LoanMortgageHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale</link:label>
    <link:label id="lab_bsprt_LoanMortgageHeldForSale_label_en-US" xlink:label="lab_bsprt_LoanMortgageHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Held-for-Sale</link:label>
    <link:label id="lab_bsprt_LoanMortgageHeldForSale_documentation_en-US" xlink:label="lab_bsprt_LoanMortgageHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanMortgageHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_LoanMortgageHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanMortgageHeldForSale" xlink:to="lab_bsprt_LoanMortgageHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_ddecd444-bb47-4b6a-8d8e-8becca7c2c8f_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_12e22a9c-907f-42fa-8327-c307fb4f5407_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems_ccd15661-3881-4473-9618-bdc23d9fc9c1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:to="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale_2ad828d8-bfa6-41da-a15e-bf2e233c73aa_negatedTerseLabel_en-US" xlink:label="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Origination and purchase of commercial mortgage loans, held for sale</link:label>
    <link:label id="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale_label_en-US" xlink:label="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Origination And Purchase Of Commercial Mortgage Loans, Held For Sale</link:label>
    <link:label id="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale_documentation_en-US" xlink:label="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Origination And Purchase Of Commercial Mortgage Loans, Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:to="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_1ace4f65-40e0-4181-bca0-71e4d56161f8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_170d3b21-6ac4-4e7a-93ed-78105dedff28_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES AND STOCKHOLDERS' EQUITY</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_3163339a-b4f4-40c3-825c-6390b1b63b7b_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_776e6947-aa35-401d-9860-23384a85b0c9_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_b87bba85-f849-4719-acbc-ba4519aa0cde_terseLabel_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans transferred from commercial mortgage loans, held for investment to real estate owned, held for sale</link:label>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferToOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferToOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferToOtherRealEstate" xlink:to="lab_us-gaap_TransferToOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InterestEarnedOnEscrows_5ee0f33d-ad5a-46eb-bd46-f7755e20f2ee_terseLabel_en-US" xlink:label="lab_bsprt_InterestEarnedOnEscrows" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest on escrows</link:label>
    <link:label id="lab_bsprt_InterestEarnedOnEscrows_label_en-US" xlink:label="lab_bsprt_InterestEarnedOnEscrows" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Earned on Escrows</link:label>
    <link:label id="lab_bsprt_InterestEarnedOnEscrows_documentation_en-US" xlink:label="lab_bsprt_InterestEarnedOnEscrows" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Earned on Escrows</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InterestEarnedOnEscrows" xlink:href="bsprt-20250930.xsd#bsprt_InterestEarnedOnEscrows"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InterestEarnedOnEscrows" xlink:to="lab_bsprt_InterestEarnedOnEscrows" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_5c78d780-7ccc-4ad2-b1c8-a3b749e9521d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net (income)/loss attributable to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_99fcc4ff-299f-4e0b-af2a-1143a796655c_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_b6dbe80f-9c8c-4af0-ac72-9ab7b5d64732_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock_16fa894f-e423-4765-beae-325a438d04ae_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Commercial Mortgage Loans Held for Investment Activity</link:label>
    <link:label id="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock_label_en-US" xlink:label="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Notes Receivable Rollforward [Table Text Block]</link:label>
    <link:label id="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Notes Receivable Rollforward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateNotesReceivableRollforwardTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:to="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_052dcd21-a8ca-4faa-9a36-08fa36253916_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Pledged assets</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_5f29dcfb-463f-409b-9528-9a08905ce165_netLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Principal Balance of Collateralized Mortgage Assets</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCollateralAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:to="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_594c22ff-1add-461c-9580-c65661f2b38c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_6d34d8f7-fc29-495c-8db1-12c9e6758937_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
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    <link:label id="lab_bsprt_InvestmentRating4Member_e82f7e8b-5e21-4d50-9696-a8b21a091b3d_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">4</link:label>
    <link:label id="lab_bsprt_InvestmentRating4Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 4 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating4Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 4 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating4Member" xlink:href="bsprt-20250930.xsd#bsprt_InvestmentRating4Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating4Member" xlink:to="lab_bsprt_InvestmentRating4Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax_9ab4e402-5ff1-4e61-8dd7-3bce911e1f3b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized loss on CLO bonds</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccumulatedGrossUnrealizedGainLossBeforeTax"/>
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    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member_66982fc7-b5ed-4c5b-baac-dfb9b5507e6c_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022-FL8 Issuer</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2022-FL8 [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2022-FL8</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:href="bsprt-20250930.xsd#bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:to="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_de576224-8a67-4f74-99f0-428a38fb6de0_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_dcbf4bc6-ca0a-4322-a52e-8b0eb7f0e6e1_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs_fdd93ad9-42cd-4604-907c-3795e2f217f1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">MSR amortization</link:label>
    <link:label id="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs_label_en-US" xlink:label="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Mortgage Servicing Rights (MSRs)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfMortgageServicingRightsMSRs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:to="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_7863b972-0abc-402c-bd9b-4fa06b03263c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease_188c0d45-c359-49b2-8f4f-56bd8a62bc16_terseLabel_en-US" xlink:label="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of properties acquired through foreclosure</link:label>
    <link:label id="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease_label_en-US" xlink:label="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Subject to or Available for Operating Lease, Number of Units, Acquired Through Foreclosures, Period Increase (Decrease)</link:label>
    <link:label id="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease_documentation_en-US" xlink:label="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property Subject to or Available for Operating Lease, Number of Units, Acquired Through Foreclosures, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease" xlink:href="bsprt-20250930.xsd#bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease" xlink:to="lab_bsprt_PropertySubjectToOrAvailableForOperatingLeaseNumberOfUnitsAcquiredThroughForeclosuresPeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_f162ba98-7aa7-40b9-96ff-e0fb123cee98_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining lease term</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseRemainingLeaseTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:to="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanRepurchaseOptionLiabilities_6cc4538c-99c9-428a-b724-cbf176de487d_terseLabel_en-US" xlink:label="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for loans eligible for repurchase</link:label>
    <link:label id="lab_bsprt_LoanRepurchaseOptionLiabilities_label_en-US" xlink:label="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Repurchase Option, Liabilities</link:label>
    <link:label id="lab_bsprt_LoanRepurchaseOptionLiabilities_documentation_en-US" xlink:label="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Repurchase Option, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanRepurchaseOptionLiabilities" xlink:href="bsprt-20250930.xsd#bsprt_LoanRepurchaseOptionLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanRepurchaseOptionLiabilities" xlink:to="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_11ece554-808c-4e80-bce5-9937f772803e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (income)/loss attributed to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityTable_dc2d411a-fdbe-40df-b198-82383c9fb18e_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Table]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityTable_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityTable" xlink:to="lab_us-gaap_LineOfCreditFacilityTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_909a0e6e-4ae9-467e-86e4-966ab9b45d9c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToMinorityShareholders" xlink:to="lab_us-gaap_PaymentsToMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTable_7afd0bb2-4d3d-45e3-8141-8aa5320afb42_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table]</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTable_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingLiabilitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTable" xlink:to="lab_us-gaap_OffsettingLiabilitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_TX_f250bae4-f2a0-4994-9c1f-21af4404f2e3_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_TX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_TX" xlink:to="lab_stpr_TX" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_13ea55f7-bd07-4514-8429-a9ec79f8d496_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WFRepoFacilityMember_4783c621-959d-4317-8569-953522dc4ba3_terseLabel_en-US" xlink:label="lab_bsprt_WFRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">WF Repo Facility</link:label>
    <link:label id="lab_bsprt_WFRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_WFRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">WF Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_WFRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_WFRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">WF Repo Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WFRepoFacilityMember" xlink:href="bsprt-20250930.xsd#bsprt_WFRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WFRepoFacilityMember" xlink:to="lab_bsprt_WFRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_94efda46-de43-4cab-95f6-7d5456aaa2fe_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Non-performing loan amortized cost at beginning of year, January 1</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_6679d791-176c-4e95-8dc4-0a3284e7ea3c_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Non-performing loan amortized cost end of period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_90d96f54-a92f-41a6-87b4-5e4fee48127a_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_ea64ac71-39b1-45fb-b799-254ef06de203_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionProFormaInformationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBankingAbstract_label_en-US" xlink:label="lab_us-gaap_MortgageBankingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Banking [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBankingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBankingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBankingAbstract" xlink:to="lab_us-gaap_MortgageBankingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_f9f539d0-7afa-436d-839c-f7a7fade34e7_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
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    <link:label id="lab_dei_TradingSymbol_547fd458-d3d5-4a4d-a6c1-d85241b3c2b2_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_07ec407a-9188-481c-b2da-05961560c912_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
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    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities_156487e6-cdbe-48c6-b805-d26b3039062e_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities, held to maturity</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Investment Securities</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Investment Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_6bec7cc9-b530-4598-8cb5-b57de492bf1c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Intangible Assets and Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Intangible Assets and Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_ec1710a2-737d-4b0b-a4a4-098151f00098_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
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    <link:label id="lab_bsprt_ReceivablesForLoanRepayment_df05c79f-b8bd-4387-b31c-caa01b7819e9_terseLabel_en-US" xlink:label="lab_bsprt_ReceivablesForLoanRepayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable for loan repayment</link:label>
    <link:label id="lab_bsprt_ReceivablesForLoanRepayment_label_en-US" xlink:label="lab_bsprt_ReceivablesForLoanRepayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables For Loan Repayment</link:label>
    <link:label id="lab_bsprt_ReceivablesForLoanRepayment_documentation_en-US" xlink:label="lab_bsprt_ReceivablesForLoanRepayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Receivables For Loan Repayment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ReceivablesForLoanRepayment" xlink:href="bsprt-20250930.xsd#bsprt_ReceivablesForLoanRepayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ReceivablesForLoanRepayment" xlink:to="lab_bsprt_ReceivablesForLoanRepayment" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_20814a45-936f-4b71-94fa-fab20ee11d3f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_f7973391-fffd-4af9-83f8-70e1f616abd8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_8764935e-af72-4374-b9a9-c988cbe0e7ec_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear_af9d7545-9129-48d9-a28e-0e551f6cccce_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_fe20219e-f1b5-4313-bab4-906e88651cca_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Purchase Price</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_b8bed970-10c3-4460-a60c-27e908a7300a_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_TreasuryNoteFuturesMember_6ff3ff8f-3ec3-4f37-a34e-9a0bc0152ee4_terseLabel_en-US" xlink:label="lab_bsprt_TreasuryNoteFuturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury note futures</link:label>
    <link:label id="lab_bsprt_TreasuryNoteFuturesMember_label_en-US" xlink:label="lab_bsprt_TreasuryNoteFuturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Note Futures [Member]</link:label>
    <link:label id="lab_bsprt_TreasuryNoteFuturesMember_documentation_en-US" xlink:label="lab_bsprt_TreasuryNoteFuturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Note Futures [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_TreasuryNoteFuturesMember" xlink:href="bsprt-20250930.xsd#bsprt_TreasuryNoteFuturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_TreasuryNoteFuturesMember" xlink:to="lab_bsprt_TreasuryNoteFuturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentOfCashForPurchasedInterests_73bbf7e4-5f13-46d0-b64f-c93254dadb6a_terseLabel_en-US" xlink:label="lab_bsprt_PaymentOfCashForPurchasedInterests" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for purchased interests</link:label>
    <link:label id="lab_bsprt_PaymentOfCashForPurchasedInterests_label_en-US" xlink:label="lab_bsprt_PaymentOfCashForPurchasedInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment Of Cash For Purchased Interests</link:label>
    <link:label id="lab_bsprt_PaymentOfCashForPurchasedInterests_documentation_en-US" xlink:label="lab_bsprt_PaymentOfCashForPurchasedInterests" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment Of Cash For Purchased Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentOfCashForPurchasedInterests" xlink:href="bsprt-20250930.xsd#bsprt_PaymentOfCashForPurchasedInterests"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentOfCashForPurchasedInterests" xlink:to="lab_bsprt_PaymentOfCashForPurchasedInterests" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_d5f82155-f93c-41be-a25f-71b9dc3a8cff_terseLabel_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded</link:label>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_label_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Loan Commitment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnfundedLoanCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:to="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_0f4b9fd3-1308-46fd-8d0c-82ca7f4e482c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_1c8d2139-7d4c-40f7-9f01-27619e40d044_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_6522efce-7f64-4093-8090-f2f65f7aaf38_periodStartLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Restricted cash, beginning of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_43b471f0-0af1-4486-b3d7-16daf6913f5d_periodEndLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Restricted cash, end of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_afdfc415-1b68-4478-be8e-6b18171b64bb_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-lived intangible, carrying value</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_d35e9044-c39a-48ac-8933-b3acf3ab051e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_544e27c6-93b3-4acf-ac55-6f168f00b840_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_4b573845-b26b-4a81-b759-e8351bc1c2d5_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_8f185c5a-9bc6-4faa-ba2e-9c06cfb08e59_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 (October - December)</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_5c64ed9e-0798-4563-b7db-d2eba5140e0e_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on sales, including fee-based services, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_label_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sales of Loans, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSalesOfLoansNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:to="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_b29f116e-2fe4-4313-814e-2e4e0c2b5c3b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities, held to maturity</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_f4dc1f24-b700-4e53-9c59-7d0847f5d378_terseLabel_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans, Held for Investment</link:label>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:to="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_df247c2f-3cbd-4f13-96fd-53463e355f7d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_97b1a36c-2dc8-4fa2-9533-da446d451cb9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets and liabilities measured at fair value, net</link:label>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_label_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Asset (Liability)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetAssetLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetAssetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetAssetLiability" xlink:to="lab_us-gaap_FairValueNetAssetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfProductInformationTable_56d173f2-a4ea-4de6-a614-a6f97d7f8a03_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfProductInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfProductInformationTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfProductInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfProductInformationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfProductInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfProductInformationTable" xlink:to="lab_us-gaap_ScheduleOfProductInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_875076b1-b91e-4b56-9336-1274403ef9f5_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Expected Amortization of MSRs</link:label>
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    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_fc074caf-7a98-43b3-aef0-e0bd0a6254b4_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
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    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember_25037a62-9849-411e-b0da-84b35bdadb0f_terseLabel_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition fees and expenses, amount capitalized</link:label>
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    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember_documentation_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition Fees And Expenses, Amount Capitalized [Member]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_eb5acfce-3ed6-4f47-bdcd-e4b43252bca2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Provision)/benefit for income tax</link:label>
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    <link:label id="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity_6dfd6a81-2cd2-49d2-8cec-93551bcdd98d_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Days to Maturity</link:label>
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    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee_43455ee2-5632-4424-9542-9faa674f298c_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of excess total return</link:label>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis_7870a028-0b2d-4b0a-b152-b5f6055864c9_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Activity, Capitalization [Axis]</link:label>
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    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_3cd1d8c2-1c2b-499c-8b07-07ec7a02b8c2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAbstract_16115904-e186-47d2-85b3-b96c49fc54a2_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:label id="lab_us-gaap_OffsettingAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAbstract" xlink:to="lab_us-gaap_OffsettingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount_297e97fc-7def-4348-aaaa-1e05e4c97afb_terseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing revenue, net</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount_label_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractuallySpecifiedServicingFeesAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:to="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition_81a33260-15ca-4596-b231-ec139ffa65fe_terseLabel_en-US" xlink:label="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance acquired in acquisition</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition_label_en-US" xlink:label="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual Allowance Acquired in Acquisition</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition_documentation_en-US" xlink:label="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual Allowance Acquired in Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:href="bsprt-20250930.xsd#bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:to="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_808a2e43-4b3f-4fd8-9a49-e450e89001f5_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill acquired during the period</link:label>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_label_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAcquiredDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:to="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest_09a71db7-87c4-41ca-a3f9-85520b597126_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total purchase consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less), and Goodwill, Less Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_72396265-300c-466d-ab92-c322f24ff495_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and Improvements</link:label>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_label_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building and Building Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingAndBuildingImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:to="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VariousLocationsMember_2b928392-bbef-4a57-acc8-3488a9d7569f_terseLabel_en-US" xlink:label="lab_bsprt_VariousLocationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Various</link:label>
    <link:label id="lab_bsprt_VariousLocationsMember_label_en-US" xlink:label="lab_bsprt_VariousLocationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Various Locations [Member]</link:label>
    <link:label id="lab_bsprt_VariousLocationsMember_documentation_en-US" xlink:label="lab_bsprt_VariousLocationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Various Geographic Locations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VariousLocationsMember" xlink:href="bsprt-20250930.xsd#bsprt_VariousLocationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VariousLocationsMember" xlink:to="lab_bsprt_VariousLocationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToDevelopSoftware_c2e65aec-26ce-4e30-833c-a55067aa2a35_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToDevelopSoftware" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of software development costs</link:label>
    <link:label id="lab_us-gaap_PaymentsToDevelopSoftware_label_en-US" xlink:label="lab_us-gaap_PaymentsToDevelopSoftware" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Develop Software</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToDevelopSoftware" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToDevelopSoftware"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToDevelopSoftware" xlink:to="lab_us-gaap_PaymentsToDevelopSoftware" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR_fda5e3a8-4e58-4904-bdca-c3226c278680_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired MSRs at July 1, 2025</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Mortgage Servicing Rights (MSR)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireMortgageServicingRightsMSR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:to="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_af205af9-832d-479f-b300-8658bb9c71d8_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
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    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets_ced0da96-7263-4fb3-a519-1ba597a56335_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Derivative Assets</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Derivative Assets</link:label>
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    <link:label id="lab_us-gaap_SalesRevenueProductLineMember_7a8a930c-29d7-4c26-813e-94ef1892751e_terseLabel_en-US" xlink:label="lab_us-gaap_SalesRevenueProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, Product and Service Benchmark</link:label>
    <link:label id="lab_us-gaap_SalesRevenueProductLineMember_label_en-US" xlink:label="lab_us-gaap_SalesRevenueProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Product and Service Benchmark [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesRevenueProductLineMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SalesRevenueProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesRevenueProductLineMember" xlink:to="lab_us-gaap_SalesRevenueProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue_5e3af85d-16b9-4f03-bb8c-3f3909a6e2aa_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, quoted market value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Quoted Market Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentQuotedMarketValue"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_53ad050c-c383-4f92-8637-e816793e7073_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in)/provided by operating activities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_56553e82-a2c6-4296-8741-447ddfb6f2ed_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale or paydown of real estate securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Debt Securities, Available-for-Sale</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_53eda3ee-d1bc-42ab-b850-3cca18dddfab_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Real estate securities, available for sale, measured at fair value, amortized cost of $82,578 and $202,894 as of September&#160;30, 2025 and December&#160;31, 2024, respectively</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_c3a70b79-d2d0-495f-ab8e-6e587708f9b8_netLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_86241021-4c37-4a71-83be-2014dd733194_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate securities, available for sale, measured at fair value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_24fdd82c-e964-466d-88c1-8101c2e4078a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of real estate owned, held for sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfOtherRealEstate"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_ed3aa737-3159-4189-a70a-ab0df220be53_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Sales/paydowns</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales"/>
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    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_e0b1315d-ec2b-458f-bc01-29cdbb5f963c_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember_db30ad66-6026-4c48-b0e1-087e064ee0de_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee or Group of Investees</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee or Group of Investees [Member]</link:label>
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    <link:label id="lab_us-gaap_RealEstateLineItems_f3d3423e-5eda-4c7a-a433-c3b6cb8aedcc_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Line Items]</link:label>
    <link:label id="lab_us-gaap_RealEstateLineItems_label_en-US" xlink:label="lab_us-gaap_RealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateLineItems" xlink:to="lab_us-gaap_RealEstateLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TypeOfReserveDomain_46a88c3a-ecc0-4aca-b2b5-e48a3b8b1991_terseLabel_en-US" xlink:label="lab_srt_TypeOfReserveDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Type of Reserve [Domain]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_6310ef94-c87b-444f-bb56-dd7935757a7d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_f9e912b7-f65d-4c83-9d90-2d8c693fb20e_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Operating</link:label>
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    <link:label id="lab_bsprt_JPMorganSecuritiesLLCMember_686ea919-e9d8-4555-8b71-793ea3988848_terseLabel_en-US" xlink:label="lab_bsprt_JPMorganSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JP Morgan Securities LLC</link:label>
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    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoTotalCompAmt"/>
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    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_321989d4-0ca5-46fe-b794-b80220fffd89_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_6b77a8c2-cf01-47cd-b0de-887c345704ec_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_26f9cb61-7748-41c2-b76a-f3c87cdd147e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, gross amounts recognized</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_f67f731f-7fcd-4a32-9ab5-6c7eafdb485b_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2025 (three months ending 12/31/2025)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_4d0dcb8d-eaf5-497f-adfe-3ec9086e8ac5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 (October - December)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FarWestMember_449e28ee-3e18-4421-8a3d-e9eaba2f726b_terseLabel_en-US" xlink:label="lab_bsprt_FarWestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Far West</link:label>
    <link:label id="lab_bsprt_FarWestMember_label_en-US" xlink:label="lab_bsprt_FarWestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Far West [Member]</link:label>
    <link:label id="lab_bsprt_FarWestMember_documentation_en-US" xlink:label="lab_bsprt_FarWestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Far West</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FarWestMember" xlink:href="bsprt-20250930.xsd#bsprt_FarWestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FarWestMember" xlink:to="lab_bsprt_FarWestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_bdb90dc8-8f12-41ba-8f6a-e070d9a72bd7_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_e8283374-ff02-4fb7-a929-85561fd4a980_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year four, originated in prior fiscal year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherRelatedPartyExpensesMember_cbdd43a6-2a2b-4cdd-91ba-05330b3abf14_terseLabel_en-US" xlink:label="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other related party expenses</link:label>
    <link:label id="lab_bsprt_OtherRelatedPartyExpensesMember_label_en-US" xlink:label="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Related Party Expenses [Member]</link:label>
    <link:label id="lab_bsprt_OtherRelatedPartyExpensesMember_documentation_en-US" xlink:label="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Related Party Expenses [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OtherRelatedPartyExpensesMember" xlink:href="bsprt-20250930.xsd#bsprt_OtherRelatedPartyExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OtherRelatedPartyExpensesMember" xlink:to="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FannieMaeMember_bbb21115-e268-4a74-a822-a55c822ef5f1_terseLabel_en-US" xlink:label="lab_bsprt_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fannie Mae</link:label>
    <link:label id="lab_bsprt_FannieMaeMember_label_en-US" xlink:label="lab_bsprt_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fannie Mae [Member]</link:label>
    <link:label id="lab_bsprt_FannieMaeMember_documentation_en-US" xlink:label="lab_bsprt_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fannie Mae</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FannieMaeMember" xlink:href="bsprt-20250930.xsd#bsprt_FannieMaeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FannieMaeMember" xlink:to="lab_bsprt_FannieMaeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_81d8f21e-0e4a-4d92-8907-f572b8b6dca9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_58b590f6-36ef-479e-90e1-5d4cdac18358_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_8d2b1828-20ca-4142-a90c-9e27f945ba2d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_45273c01-b5e1-4fc6-93e7-a34b8175fefe_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock distributions</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_a3464f06-4a15-4973-ad47-8d9a7b1e1f95_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAsset_905f24aa-b9bf-4fd6-90ea-265ac369b017_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights, net</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_c6f9d747-8286-4f41-8e93-16321c5da938_periodStartLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance, as of January 1, 2025</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_cda7638f-e7f4-4305-9604-46e69647f811_periodEndLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance, as of September 30, 2025</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_label_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAsset" xlink:to="lab_us-gaap_ServicingAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_f330fa3f-11f5-4d09-b62f-8236ef0571f0_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans eligible for repurchase</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentAggregateCost_b1d742c7-4a6f-42e2-ad52-3746059d2d12_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentAggregateCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Aggregate Cost</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentAggregateCost_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentAggregateCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Aggregate Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentAggregateCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentAggregateCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentAggregateCost" xlink:to="lab_us-gaap_EquityMethodInvestmentAggregateCost" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RockyMountainMember_6867006c-2417-4116-9da1-8108a9ef7128_terseLabel_en-US" xlink:label="lab_bsprt_RockyMountainMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rocky Mountain</link:label>
    <link:label id="lab_bsprt_RockyMountainMember_label_en-US" xlink:label="lab_bsprt_RockyMountainMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rocky Mountain [Member]</link:label>
    <link:label id="lab_bsprt_RockyMountainMember_documentation_en-US" xlink:label="lab_bsprt_RockyMountainMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rocky Mountain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RockyMountainMember" xlink:href="bsprt-20250930.xsd#bsprt_RockyMountainMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RockyMountainMember" xlink:to="lab_bsprt_RockyMountainMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableLoanServicingPortfolio_b5ca52ac-5cf2-4888-9969-f81e624a62ae_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing portfolio</link:label>
    <link:label id="lab_bsprt_FinancingReceivableLoanServicingPortfolio_label_en-US" xlink:label="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Loan Servicing Portfolio</link:label>
    <link:label id="lab_bsprt_FinancingReceivableLoanServicingPortfolio_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Loan Servicing Portfolio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:href="bsprt-20250930.xsd#bsprt_FinancingReceivableLoanServicingPortfolio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:to="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentForAmortization_e89d0a09-d045-4a99-87c5-fc2d83cabf44_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentForAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
    <link:label id="lab_us-gaap_AdjustmentForAmortization_label_en-US" xlink:label="lab_us-gaap_AdjustmentForAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentForAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentForAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentForAmortization" xlink:to="lab_us-gaap_AdjustmentForAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_036ffbef-ece3-4a7f-9ba2-dc47f8382791_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions from non-controlling interest</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:to="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyDisclosures_42913927-b28d-4c4a-91c1-05707d74ca68_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyDisclosures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Loss Sharing</link:label>
    <link:label id="lab_us-gaap_LossContingencyDisclosures_label_en-US" xlink:label="lab_us-gaap_LossContingencyDisclosures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyDisclosures" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyDisclosures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyDisclosures" xlink:to="lab_us-gaap_LossContingencyDisclosures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_6ce82003-c443-4a34-afe2-1b183e01f885_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest, ownership percentage by noncontrolling owners</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate_c3bb31ba-a730-4631-9457-566eac814997_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension period on initial maturity date</link:label>
    <link:label id="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate_label_en-US" xlink:label="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension On Initial Maturity Date</link:label>
    <link:label id="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension on Initial Maturity Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:href="bsprt-20250930.xsd#bsprt_DebtInstrumentExtensionOnInitialMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:to="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_66f203c7-0f80-4a06-bd81-aaa5f37a8a43_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NewPointJVLLCMember_7e7a951b-4043-4ab7-9e21-024760bbbb66_terseLabel_en-US" xlink:label="lab_bsprt_NewPointJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NewPoint JV LLC</link:label>
    <link:label id="lab_bsprt_NewPointJVLLCMember_label_en-US" xlink:label="lab_bsprt_NewPointJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NewPoint JV LLC [Member]</link:label>
    <link:label id="lab_bsprt_NewPointJVLLCMember_documentation_en-US" xlink:label="lab_bsprt_NewPointJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NewPoint JV LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NewPointJVLLCMember" xlink:href="bsprt-20250930.xsd#bsprt_NewPointJVLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NewPointJVLLCMember" xlink:to="lab_bsprt_NewPointJVLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure_14581d8a-6281-4173-b00a-ab66c254dd4b_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgages Held For Sale Fair Value Disclosure</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgages Held For Sale Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate_ed8db91f-1bcb-4a8e-b3e8-37705143c36d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on other real estate investments</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gains (Losses) on Sales of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnSalesOfOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:to="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SouthwestMember_4125433e-bfb0-47cb-9716-9cb0eccb8f3f_terseLabel_en-US" xlink:label="lab_bsprt_SouthwestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Southwest</link:label>
    <link:label id="lab_bsprt_SouthwestMember_label_en-US" xlink:label="lab_bsprt_SouthwestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Southwest [Member]</link:label>
    <link:label id="lab_bsprt_SouthwestMember_documentation_en-US" xlink:label="lab_bsprt_SouthwestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Southwest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SouthwestMember" xlink:href="bsprt-20250930.xsd#bsprt_SouthwestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SouthwestMember" xlink:to="lab_bsprt_SouthwestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_3b98f9a9-0696-42fd-942f-d1974e05a4d0_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Avg. Life (in Years)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Remaining Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_6c2f7fa7-043a-4bf9-9289-29bed27143d4_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_7be40325-5130-4c81-9106-376dea0148ad_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDeposits" xlink:to="lab_us-gaap_InterestExpenseDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_17e7561b-1e3d-4595-95d7-cb0c7deb0f3b_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_bc564b05-3827-4f79-af8e-512691dd4175_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock_99597afc-1f6e-40e9-a299-a8c3c0be2b83_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Future Minimum Payments to be Received</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale_56fb6114-2fab-48ed-bf1b-591b643e7e78_terseLabel_en-US" xlink:label="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seller-based financing on sales of real estate owned, held for sale</link:label>
    <link:label id="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale_label_en-US" xlink:label="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Seller Based Financing On Sales Of Real Estate Owned Held For Sale</link:label>
    <link:label id="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale_documentation_en-US" xlink:label="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Seller Based Financing On Sales Of Real Estate Owned Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:to="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits_a2084571-e698-45ed-8da7-60772f033724_terseLabel_en-US" xlink:label="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Add: Net income/(loss) from non-controlling interest - OP Units</link:label>
    <link:label id="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits_label_en-US" xlink:label="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income/(Loss) From Non-Controlling Interest - OP Units</link:label>
    <link:label id="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits_documentation_en-US" xlink:label="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income/(Loss) From Non-Controlling Interest - OP Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:href="bsprt-20250930.xsd#bsprt_NetIncomeLossFromNonControllingInterestOPUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:to="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_7ea91be6-cabc-4f58-b514-0ab1120e1bf6_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_29915012-e22a-4c14-a5a9-a7be80239793_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_e1ff71c0-13c6-4ebb-9dd9-9b26332ca9d6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_3b4eb616-84dd-4318-9d87-a38386993bd7_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of cash flow information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Elements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowElementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_fe7d9bbe-e73b-409b-8339-6652abf9924d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allocation by Risk Rating</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses_bdcdc3e5-9673-46f0-abba-f68a1a8bc453_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Before Allowance For Credit Losses</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Before Allowance For Credit Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:href="bsprt-20250930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale_c9b438bf-748d-48a9-a8c8-237aa9ad62af_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Origination of commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Origination, Loan, Mortgage, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:to="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_c5eab8f1-95d8-41f0-ac3c-1c6fff49ddb2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OfficeBuildingMember_21f34c22-d64f-44e6-b93c-dc7061f59561_terseLabel_en-US" xlink:label="lab_srt_OfficeBuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Office</link:label>
    <link:label id="lab_srt_OfficeBuildingMember_label_en-US" xlink:label="lab_srt_OfficeBuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Office Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OfficeBuildingMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OfficeBuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OfficeBuildingMember" xlink:to="lab_srt_OfficeBuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateDispositions_dacb58f1-b73c-4d29-94fd-81cafa1fc650_terseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dispositions</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateDispositions_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Dispositions</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateDispositions_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Dispositions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateDispositions" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansOnRealEstateDispositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateDispositions" xlink:to="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_5e20b332-5d02-4098-9489-c54f7c51dad6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward_3e1d2007-40b8-4b81-8835-9e1a0a6e3a96_terseLabel_en-US" xlink:label="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward_label_en-US" xlink:label="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Movement in Mortgage Loans on Real Estate [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MovementInMortgageLoansOnRealEstateRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:to="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_edbe0134-8faf-41ef-bdc8-d2195fcf45d3_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_05cf0a8f-3a6c-4af6-993f-6147505a7759_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_0c7a7a9d-b71e-4589-b407-8e1ca7d8b84e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeAxis"/>
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    <link:label id="lab_bsprt_UnsecuredSeniorNotesIMember_f7d4f21b-566f-41b9-a739-727444efbaf5_terseLabel_en-US" xlink:label="lab_bsprt_UnsecuredSeniorNotesIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Senior Notes I</link:label>
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    <link:label id="lab_us-gaap_LossContingencyAccrualProvision_ccdda415-d3ff-48b8-bd59-6e6ddad7f146_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualProvision" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for loss sharing</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualProvision_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualProvision" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual, Provision</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualProvision" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyAccrualProvision"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualProvision" xlink:to="lab_us-gaap_LossContingencyAccrualProvision" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_b09d7f15-84c3-49cc-b674-4c8a6d2e237c_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
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    <link:label id="lab_us-gaap_RealEstateAcquiredThroughForeclosure_41d48d29-5053-488b-a300-5be1a5a97f34_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned, net of depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateAcquiredThroughForeclosure_label_en-US" xlink:label="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Acquired Through Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAcquiredThroughForeclosure"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_6fe67857-9c71-4512-b2f7-607dfa8a2474_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-lived intangible, carrying value</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
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    <link:label id="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations_ca44f5dc-30ef-4e9a-b714-affe7a01d805_terseLabel_en-US" xlink:label="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing obligations</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:href="bsprt-20250930.xsd#bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations"/>
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    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
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    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions_bda95bad-0b65-4d4e-8ce0-dfdb02124f2b_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Additions</link:label>
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    <link:label id="lab_dei_EntityAddressAddressLine1_4ef10e34-7131-45b3-a911-adaca0d8afc7_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_c796f17a-85e6-490c-8846-7e92bd8f9727_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income/(Loss)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_edbf2520-7bc4-423d-8353-27d67b64a8db_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares canceled for tax withholding on vested equity rewards (in shares)</link:label>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_b73c9c09-d6f2-42d4-a17c-f2bcee06104a_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InternalCreditAssessmentAxis"/>
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    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
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    <link:label id="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses_aca41550-9981-4256-b1bf-b8d4d3c14196_terseLabel_en-US" xlink:label="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current eExpected credit losses</link:label>
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    <link:label id="lab_srt_OwnershipAxis_1bfae7dc-0163-4fd7-a24c-3c18c3858654_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock_05616fb1-1361-476d-9035-1e8610c5c01b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loans on Nonaccrual Status</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_359fce0d-4063-4bd0-8f8b-174701bbfd3a_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability_42acb4db-96c9-4081-b301-748dc169145c_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan repurchase option liability</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Loan Repurchase Option Liability</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Loan Repurchase Option Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold_92db2bff-0130-4006-ba26-3a3c79a08a38_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated performance fee, percent that total return exceeds per year</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold_label_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Performance Fee Total Return Threshold</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold_documentation_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Performance Fee Total Return Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:href="bsprt-20250930.xsd#bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:to="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfUnitsInRealEstateProperty_92839521-5b12-4e7c-82ab-5d0bf3687a50_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfUnitsInRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of property</link:label>
    <link:label id="lab_us-gaap_NumberOfUnitsInRealEstateProperty_label_en-US" xlink:label="lab_us-gaap_NumberOfUnitsInRealEstateProperty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Units in Real Estate Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfUnitsInRealEstateProperty" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfUnitsInRealEstateProperty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfUnitsInRealEstateProperty" xlink:to="lab_us-gaap_NumberOfUnitsInRealEstateProperty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyLoansReceivablePolicy_9e5613eb-db03-47a5-a409-70842a87a4ef_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyLoansReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loan Repurchase</link:label>
    <link:label id="lab_us-gaap_PolicyLoansReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_PolicyLoansReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policy Loans Receivable, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyLoansReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyLoansReceivablePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyLoansReceivablePolicy" xlink:to="lab_us-gaap_PolicyLoansReceivablePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_ecd25e2b-3eca-4b6c-9881-7338ab18bfe9_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_7c3d51fd-c7df-4f00-be15-926f5d0f9c7e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of NewPoint Holdings JV LLC</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_a8726210-345e-47b2-ac65-4db9738131bf_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase of NewPoint Holdings JV LLC</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_400f2b2c-c52a-491f-8b92-2bccbdfd6daa_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividend rate percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:to="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_b2ad243d-d6e5-4a60-9b71-ab68b7bba46b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_1b95a5cf-37ad-4b43-a8fc-593c1066b8ce_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Intangible Assets</link:label>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Intangible Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIntangibleAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIntangibleAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIntangibleAssetsMember" xlink:to="lab_us-gaap_OtherIntangibleAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_ced1f98c-2a73-48ec-8a64-feec14f86fd5_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_ab95eeb9-518c-486b-94f6-21f74cc635a6_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_90de8d8d-a5fc-4a68-a9b9-8e870d53a057_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_850c0509-f356-4b90-973c-03f910ed52f0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:to="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_aa7cd77b-7028-4f6f-950d-44fa66eaa73c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_1fe9eff9-5f5b-4e14-96ed-b111fc219540_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_1601d024-d98c-4ae5-97af-f5eb96f969e6_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentsToAcquireRealEstateOwned_96e6a865-39de-4197-9a2f-cbc90e197854_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of real estate owned and capital expenditures</link:label>
    <link:label id="lab_bsprt_PaymentsToAcquireRealEstateOwned_label_en-US" xlink:label="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Real Estate Owned</link:label>
    <link:label id="lab_bsprt_PaymentsToAcquireRealEstateOwned_documentation_en-US" xlink:label="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentsToAcquireRealEstateOwned" xlink:href="bsprt-20250930.xsd#bsprt_PaymentsToAcquireRealEstateOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentsToAcquireRealEstateOwned" xlink:to="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale_29ef00e8-426f-48c2-83d8-c9446cc6596e_terseLabel_en-US" xlink:label="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized gain/(loss) included in earnings</link:label>
    <link:label id="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale_label_en-US" xlink:label="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings, Sale of Commercial Mortgage Loan Held For Sale</link:label>
    <link:label id="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale_documentation_en-US" xlink:label="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Earnings, Sale of Commercial Mortgage Loan Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:to="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_148462f2-4c87-41c0-8b84-fd4f689ecd02_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StraightLineRent_8d5159a0-dac5-4033-90f1-1ad5dcae143d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StraightLineRent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Straight line rental income</link:label>
    <link:label id="lab_us-gaap_StraightLineRent_label_en-US" xlink:label="lab_us-gaap_StraightLineRent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Straight Line Rent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StraightLineRent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StraightLineRent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StraightLineRent" xlink:to="lab_us-gaap_StraightLineRent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_41e401d1-74f2-4f1e-8dff-8f060928dc81_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax_ddab5e82-9354-4b45-b75f-510709992a09_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gain on CLO bonds</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Net Unrealized Gain (Loss), before Tax</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Net Unrealized Gain (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:href="bsprt-20250930.xsd#bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable_64ec1c54-76fb-4ab2-bcfe-76b04e053684_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Interest Payable</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FifthThirdWHLineOfCreditMember_039c675a-1ddf-46ac-a0cb-637192576baa_terseLabel_en-US" xlink:label="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fifth Third WH Line of Credit</link:label>
    <link:label id="lab_bsprt_FifthThirdWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fifth Third WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_FifthThirdWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fifth Third WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FifthThirdWHLineOfCreditMember" xlink:href="bsprt-20250930.xsd#bsprt_FifthThirdWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FifthThirdWHLineOfCreditMember" xlink:to="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentGross_e121f1ff-cfef-4906-b60e-3bfc533c31c3_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned, gross</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentGross_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Gross</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentGross_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateOwnedHeldForInvestmentGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:to="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_acd145c6-112a-444b-b872-f4a1a65db100_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income</link:label>
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    <link:label id="lab_bsprt_CommercialMortgageLoansHeldForSaleMember_74daa1c9-1540-4047-b246-7688796cb83e_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Held For Sale</link:label>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain_546f58fd-d3d8-4ac7-82c1-7043c4cea5a0_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationActivityCapitalizationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Activity, Capitalization [Domain]</link:label>
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    <link:label id="lab_us-gaap_RealEstateInvestmentsJointVentures_afde4e3b-ffdb-46f5-a51a-cbf157cc6bc5_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentsJointVentures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investments, joint ventures</link:label>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_1cd8557c-5f6b-46cb-afa1-63ed0714af32_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_c722c681-7d93-408a-83f9-2f2320608c4f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansMember_7234ad67-588b-40e5-8965-20c300d70f14_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans [Member]</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansMember_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansMember" xlink:href="bsprt-20250930.xsd#bsprt_CommercialMortgageLoansMember"/>
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    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_79a1fba8-3a8f-4276-82c8-30e6c12b53cb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
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    <link:label id="lab_us-gaap_OperatingLeasePayments_f82cfb8b-8f02-471f-8d28-b27bbf4e739f_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash outflows from operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_919bf3ae-d349-4832-98a6-f49d6a22c5a0_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_e01d7c51-ac8a-4920-a5e9-ed5c20191ddf_verboseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Distribution payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_6a6848b3-8133-4919-8268-84a6c36d1ada_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to common shareholders (diluted)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BasicNumeratorAbstract_43a551f3-7057-47e0-88c2-07e41b69ff71_terseLabel_en-US" xlink:label="lab_bsprt_BasicNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic Numerator</link:label>
    <link:label id="lab_bsprt_BasicNumeratorAbstract_label_en-US" xlink:label="lab_bsprt_BasicNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basic Numerator [Abstract]</link:label>
    <link:label id="lab_bsprt_BasicNumeratorAbstract_documentation_en-US" xlink:label="lab_bsprt_BasicNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Numerator [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BasicNumeratorAbstract" xlink:href="bsprt-20250930.xsd#bsprt_BasicNumeratorAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BasicNumeratorAbstract" xlink:to="lab_bsprt_BasicNumeratorAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable_b9a75b8c-b0e2-4dd4-830c-a1e4dff27c98_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Assets Sold under Agreements to Repurchase [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Sold under Agreement to Repurchase [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:to="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_85ac3fbd-3193-4e57-8934-d903dabdb329_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_008a4680-1e86-4a7d-b15f-28b38ca8630e_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_493f48b9-c4be-41c7-8016-d854a9961764_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted weighted average shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_460c99a1-68c5-467d-881b-2f71cbe17d63_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common shares outstanding for diluted earnings per share (in shares)</link:label>
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    <link:label id="lab_bsprt_LubbockTexasMember_4677fc55-27ad-4a95-9c00-29c4d9f6882c_terseLabel_en-US" xlink:label="lab_bsprt_LubbockTexasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lubbock, TX</link:label>
    <link:label id="lab_bsprt_LubbockTexasMember_label_en-US" xlink:label="lab_bsprt_LubbockTexasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lubbock, Texas [Member]</link:label>
    <link:label id="lab_bsprt_LubbockTexasMember_documentation_en-US" xlink:label="lab_bsprt_LubbockTexasMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lubbock, Texas</link:label>
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    <link:label id="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities_818ba25e-c2db-4ab2-b4c7-02747261e471_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale/(purchase) of derivative instruments</link:label>
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    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfWhollyOwnedSubsidiaries_b7adb5ea-238c-4d67-893b-c8fcbcb2588e_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfWhollyOwnedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of wholly owned subsidiaries</link:label>
    <link:label id="lab_bsprt_NumberOfWhollyOwnedSubsidiaries_label_en-US" xlink:label="lab_bsprt_NumberOfWhollyOwnedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Wholly Owned Subsidiaries</link:label>
    <link:label id="lab_bsprt_NumberOfWhollyOwnedSubsidiaries_documentation_en-US" xlink:label="lab_bsprt_NumberOfWhollyOwnedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Wholly Owned Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfWhollyOwnedSubsidiaries" xlink:href="bsprt-20250930.xsd#bsprt_NumberOfWhollyOwnedSubsidiaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfWhollyOwnedSubsidiaries" xlink:to="lab_bsprt_NumberOfWhollyOwnedSubsidiaries" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_32ebc4fd-8949-4974-857e-c05d51ce4ff4_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_ec8bbedf-55de-4182-a155-cb40267948ac_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_47575755-60e2-49e0-ade1-a27267ca037f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity interest acquired, percentage</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Voting Equity Interest Acquired, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue_2dba4439-98e9-4025-8077-5ae2689384d0_negatedLabel_en-US" xlink:label="lab_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Realized (gain)/loss on sale of commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue_label_en-US" xlink:label="lab_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss) On Sale Of Mortgage Loans Held For Sale Measured At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:href="bsprt-20250930.xsd#bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:to="lab_bsprt_RealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OriginatedMortgageServicingRightsRevenue_ca1153e6-6f6a-444a-abb2-7d746fabcf4f_terseLabel_en-US" xlink:label="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_bsprt_OriginatedMortgageServicingRightsRevenue_label_en-US" xlink:label="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Originated Mortgage Servicing Rights Revenue</link:label>
    <link:label id="lab_bsprt_OriginatedMortgageServicingRightsRevenue_documentation_en-US" xlink:label="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Originated Mortgage Servicing Rights Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:href="bsprt-20250930.xsd#bsprt_OriginatedMortgageServicingRightsRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:to="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage_4e72fe27-cdb1-47bd-b0aa-f624fbe78ae8_terseLabel_en-US" xlink:label="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average servicing fee (as a percent)</link:label>
    <link:label id="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage_label_en-US" xlink:label="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Percentage</link:label>
    <link:label id="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage_documentation_en-US" xlink:label="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:href="bsprt-20250930.xsd#bsprt_ContractuallySpecifiedServicingFeesPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:to="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_9ef55bc8-e164-46bc-947d-279e29d9e299_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AffordableMember_2b2ddb78-3253-435b-b175-c63cf2a19353_terseLabel_en-US" xlink:label="lab_bsprt_AffordableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affordable</link:label>
    <link:label id="lab_bsprt_AffordableMember_label_en-US" xlink:label="lab_bsprt_AffordableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affordable [Member]</link:label>
    <link:label id="lab_bsprt_AffordableMember_documentation_en-US" xlink:label="lab_bsprt_AffordableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Affordable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AffordableMember" xlink:href="bsprt-20250930.xsd#bsprt_AffordableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AffordableMember" xlink:to="lab_bsprt_AffordableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_ed6bd02f-e76f-4d94-a32f-cce8bd66ac27_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LucidPrimeFundMember_61bf6c29-0a4b-4e7a-aa67-30295ad487de_terseLabel_en-US" xlink:label="lab_bsprt_LucidPrimeFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lucid Prime Fund</link:label>
    <link:label id="lab_bsprt_LucidPrimeFundMember_label_en-US" xlink:label="lab_bsprt_LucidPrimeFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lucid Prime Fund [Member]</link:label>
    <link:label id="lab_bsprt_LucidPrimeFundMember_documentation_en-US" xlink:label="lab_bsprt_LucidPrimeFundMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lucid Prime Fund</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LucidPrimeFundMember" xlink:href="bsprt-20250930.xsd#bsprt_LucidPrimeFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LucidPrimeFundMember" xlink:to="lab_bsprt_LucidPrimeFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_a62726f0-ad32-40d2-a229-a0bbe2635871_terseLabel_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedules of Concentration of Risk, by Risk Factor</link:label>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_label_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedules of Concentration of Risk, by Risk Factor [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:to="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedMember_642cf88b-54b2-46e9-a3a6-f75376c5015e_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedMember_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Member]</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedMember_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedMember" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateOwnedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedMember" xlink:to="lab_bsprt_RealEstateOwnedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_cca4d07c-d2c6-4a42-a727-5c63ae5ded5e_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions_02b235f6-f7dc-4aa1-ae4c-9bac516ad6ea_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of positions with gross unrealized (loss) gain period less than 12 months</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Gross Gain (Loss) Position, Number of Positions</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Gross Gain (Loss) Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:href="bsprt-20250930.xsd#bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_0cd49c1d-7bba-4f62-a48a-785e16a5d001_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InitialRiskRatingOfLoans_f474234e-9730-448e-95a7-e09bd05a8980_terseLabel_en-US" xlink:label="lab_bsprt_InitialRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial risk rating</link:label>
    <link:label id="lab_bsprt_InitialRiskRatingOfLoans_label_en-US" xlink:label="lab_bsprt_InitialRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial Risk Rating Of Loans</link:label>
    <link:label id="lab_bsprt_InitialRiskRatingOfLoans_documentation_en-US" xlink:label="lab_bsprt_InitialRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial Risk Rating of Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InitialRiskRatingOfLoans" xlink:href="bsprt-20250930.xsd#bsprt_InitialRiskRatingOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InitialRiskRatingOfLoans" xlink:to="lab_bsprt_InitialRiskRatingOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember_1f4ffbc3-683a-4878-9001-77f6d69fc265_terseLabel_en-US" xlink:label="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 90 days past due</link:label>
    <link:label id="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember_label_en-US" xlink:label="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Less Than 90 Days Past Due [Member]</link:label>
    <link:label id="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember_documentation_en-US" xlink:label="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Asset, Less Than 90 Days Past Due</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:href="bsprt-20250930.xsd#bsprt_FinancialAssetLessThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:to="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_e36ef274-f345-441a-b27a-2d678dc0ccdd_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Including Not Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_1a6768a2-72b6-48ca-aa96-f7127637033d_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_898f7faf-f9dc-40e9-b1f5-5dd9c2afae3b_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, Beginning of Period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_d8fa7f6b-df7a-4971-ad98-2599124404d0_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, End of Period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod_2135c3ef-6817-4dcc-a90f-4b25cb8d767d_terseLabel_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of stock, preferred stock to common stock, notice period</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod_label_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock To Common Stock, Notice Period</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod_documentation_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock To Common Stock, Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:href="bsprt-20250930.xsd#bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:to="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CMBSBondsMember_dd3e1c04-f3ef-449b-9cb2-d5aecbfac159_terseLabel_en-US" xlink:label="lab_bsprt_CMBSBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS Bonds</link:label>
    <link:label id="lab_bsprt_CMBSBondsMember_label_en-US" xlink:label="lab_bsprt_CMBSBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CMBS Bonds [Member]</link:label>
    <link:label id="lab_bsprt_CMBSBondsMember_documentation_en-US" xlink:label="lab_bsprt_CMBSBondsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CMBS Bonds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CMBSBondsMember" xlink:href="bsprt-20250930.xsd#bsprt_CMBSBondsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CMBSBondsMember" xlink:to="lab_bsprt_CMBSBondsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_cf713e73-7c98-4d03-8bcd-0184fe912bf2_periodStartLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Amortized cost, beginning of period</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_4de677a4-7e01-4a02-b005-ab8bd257d6db_periodEndLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Amortized cost, end of period</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Commercial and Consumer, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_795c9f6b-a82f-423b-acf2-5cbeed798c6f_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_3ec79c59-b3ab-4a95-9ec0-c8ec2d442b51_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level III</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_ee3c487a-7d8e-4a14-88bf-3215d924bb0e_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesTable_7ca9d442-f970-42b6-96b9-d775b1904894_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_cb8c4729-c33d-4e59-a12d-267c70401a8d_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_763d4fd3-966c-49ed-83e1-29970ecd2716_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayable_27ed6476-2188-468e-9875-b2138f9f6256_netLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Mortgage note payable</link:label>
    <link:label id="lab_us-gaap_NotesPayable_597be315-8133-4c96-a3aa-19579633d8aa_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
    <link:label id="lab_us-gaap_NotesPayable_2125d407-4cfe-4b4f-8c46-27aa674928ca_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_us-gaap_NotesPayable_label_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayable" xlink:to="lab_us-gaap_NotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableLeaseCost_3fcd89b8-6c11-4144-807e-4fe7ed638e66_terseLabel_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable lease cost</link:label>
    <link:label id="lab_us-gaap_VariableLeaseCost_label_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableLeaseCost" xlink:to="lab_us-gaap_VariableLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_ed4f9163-9fa0-4e8d-b0b2-58dbbbf1aa4e_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Revenue/Investment Income</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SubsidiaryAxis_344b2354-adac-4af6-a8b5-ec9196a8c11b_terseLabel_en-US" xlink:label="lab_bsprt_SubsidiaryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary [Axis]</link:label>
    <link:label id="lab_bsprt_SubsidiaryAxis_label_en-US" xlink:label="lab_bsprt_SubsidiaryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary [Axis]</link:label>
    <link:label id="lab_bsprt_SubsidiaryAxis_documentation_en-US" xlink:label="lab_bsprt_SubsidiaryAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsidiary</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SubsidiaryAxis" xlink:href="bsprt-20250930.xsd#bsprt_SubsidiaryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SubsidiaryAxis" xlink:to="lab_bsprt_SubsidiaryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale_08f64987-d736-41bd-ae7c-418d5888402c_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loan, held for sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale, Loan, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfLoansHeldForSale" xlink:to="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_0ae1829e-7383-4a8a-89c0-08509f4fad64_terseLabel_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets Acquired</link:label>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_f55feb7f-cd60-41a4-a246-c2730d347a69_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LitigationSettlementInterest_c3ef7d31-8a4d-4829-80cd-082a03c72cb4_terseLabel_en-US" xlink:label="lab_us-gaap_LitigationSettlementInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation settlement</link:label>
    <link:label id="lab_us-gaap_LitigationSettlementInterest_label_en-US" xlink:label="lab_us-gaap_LitigationSettlementInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Settlement Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LitigationSettlementInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LitigationSettlementInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LitigationSettlementInterest" xlink:to="lab_us-gaap_LitigationSettlementInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_95a74a84-a8d6-4e3b-bacf-1e4def82471c_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share repurchase program, authorized amount</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_dc93da52-daa0-4e69-bd35-adffb92d9739_periodStartLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at January 1, 2025</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_44927c1f-c4e8-43a4-b139-2ae2c47a1013_periodEndLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at September 30, 2025</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyAccrualAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned_4e402d57-5b8c-4235-a715-d12a67af2b32_negatedTerseLabel_en-US" xlink:label="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Gain)/loss from other real estate investments</link:label>
    <link:label id="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned_label_en-US" xlink:label="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) On Other Real Estate Owned</link:label>
    <link:label id="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned_documentation_en-US" xlink:label="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) on Other Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:href="bsprt-20250930.xsd#bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:to="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum_2939b9a2-b7d0-4a04-82e5-c8c2064b168b_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum annual subordinated performance fee payable percent of total return</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum_label_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Participation In Asset Sale Fee Maximum</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum_documentation_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Participation In Asset Sale Fee Maximum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:href="bsprt-20250930.xsd#bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:to="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AtlasRepoFacilityMember_bc10c97a-0b9a-4467-b16c-a96fe0de5be0_terseLabel_en-US" xlink:label="lab_bsprt_AtlasRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Atlas Repo Facility</link:label>
    <link:label id="lab_bsprt_AtlasRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_AtlasRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Atlas Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_AtlasRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_AtlasRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Atlas Repo Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AtlasRepoFacilityMember" xlink:href="bsprt-20250930.xsd#bsprt_AtlasRepoFacilityMember"/>
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    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_5a6bd5e5-4f52-415e-b794-d64c9d0dfd0d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares cancelled for tax withholding on vested equity rewards</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral_da0ade0d-151a-4e4e-b296-110f92dccfed_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged investment securities</link:label>
    <link:label id="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral_label_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Loaned, Fair Value of Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesLoanedFairValueOfCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:to="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_b94e6dda-aa42-41e0-99b2-a39b71c65801_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to common shareholders (basic)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_9ebb3583-f59e-4021-8140-99fefe4d0cc5_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to common stockholders (basic)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_7783cd88-e3e2-46b7-85ca-93037b706513_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic Earnings (Loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue_5fbbef3e-4b77-48d9-98ab-618a76000d10_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Removal of non-performing loan amortized cost</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, Removal Of Carrying Value</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, Removal Of Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:href="bsprt-20250930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GainLossOnOtherRealEstateInvestments_c208374c-e836-4e7e-9799-282a9d770349_terseLabel_en-US" xlink:label="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on other real estate investments</link:label>
    <link:label id="lab_bsprt_GainLossOnOtherRealEstateInvestments_label_en-US" xlink:label="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Other Real Estate Investments</link:label>
    <link:label id="lab_bsprt_GainLossOnOtherRealEstateInvestments_documentation_en-US" xlink:label="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Other Real Estate Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GainLossOnOtherRealEstateInvestments" xlink:href="bsprt-20250930.xsd#bsprt_GainLossOnOtherRealEstateInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GainLossOnOtherRealEstateInvestments" xlink:to="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_8b460436-aaf2-42bf-9406-8862bae37b48_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments, Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_7b576bbc-3f15-4302-8aad-6a82444d8da4_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherRealEstatePropertyMember_181446ec-73dd-4512-a157-2346f78fa9ef_terseLabel_en-US" xlink:label="lab_bsprt_OtherRealEstatePropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_62bee770-2ed8-4355-ae07-8492e485b5c0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level I</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCredit_6d2448b7-2396-4c87-94fe-be70c3dbb0bc_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount Outstanding</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_TaxableREITSubsidiariesMember_c73d05b0-2738-4a28-bff5-580607938f21_terseLabel_en-US" xlink:label="lab_bsprt_TaxableREITSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TRS</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_bsprt_TaxableREITSubsidiariesMember" xlink:href="bsprt-20250930.xsd#bsprt_TaxableREITSubsidiariesMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_f4dde485-4fcb-4cdf-bfc4-b6cbe55f8b31_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions, by Related Party [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_6c787a56-9abd-4f28-8a82-cc4064a5ee41_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
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    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member_177f8f9c-a8b9-4f56-a76c-79e5a448b53e_terseLabel_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Note III(17)</link:label>
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    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member_documentation_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note III, Maturing September 2036</link:label>
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    <link:label id="lab_srt_MultifamilyMember_b6dbdc1f-c955-4c83-95a0-2448557a256d_terseLabel_en-US" xlink:label="lab_srt_MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multifamily</link:label>
    <link:label id="lab_srt_MultifamilyMember_label_en-US" xlink:label="lab_srt_MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multifamily [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MultifamilyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MultifamilyMember" xlink:to="lab_srt_MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_cb1fe6c4-edba-403f-9945-e2bf02209b1b_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of non - cash flow information:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_11965c18-973b-43cb-9145-f0c5b7990fe6_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AOCIAttributableToParentNetOfTaxRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:to="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_4b592345-5a0f-498f-bb07-44554b980e56_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate UPB</link:label>
    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_label_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableHeldForSaleAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansReceivableHeldForSaleAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableHeldForSaleAmount" xlink:to="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock_57b8f236-8a86-45f0-81c8-4b4ba19a76d1_terseLabel_en-US" xlink:label="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage Loans, Held for Sale</link:label>
    <link:label id="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock_label_en-US" xlink:label="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage Loans, Held for Sale [Table Text Block]</link:label>
    <link:label id="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage Loans, Held for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:href="bsprt-20250930.xsd#bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock"/>
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    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_ff8fe111-2cd2-4c56-8994-00445d88c0b8_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_a75760a2-f557-4363-8074-0f2ca298adf2_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures Disclosure [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_5178fe8c-03b8-4afd-a994-14d1a01c4746_totalLabel_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) applicable to common stock, basic</link:label>
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    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock_006bf295-b635-47d6-9f53-b1e605b5fc38_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Owned, Held For Investment</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_1e855757-d075-44b8-b14d-2833dccadb96_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
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    <link:label id="lab_bsprt_HospitalityPropertyMember_272fb1eb-6c15-40f4-9010-a36456134d08_terseLabel_en-US" xlink:label="lab_bsprt_HospitalityPropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hospitality Property</link:label>
    <link:label id="lab_bsprt_HospitalityPropertyMember_label_en-US" xlink:label="lab_bsprt_HospitalityPropertyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hospitality Property [Member]</link:label>
    <link:label id="lab_bsprt_HospitalityPropertyMember_documentation_en-US" xlink:label="lab_bsprt_HospitalityPropertyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hospitality Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_HospitalityPropertyMember" xlink:href="bsprt-20250930.xsd#bsprt_HospitalityPropertyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_HospitalityPropertyMember" xlink:to="lab_bsprt_HospitalityPropertyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GarfieldPGJVHoldCoLLCMember_f34aafaa-f505-4616-adc2-fe4e8c96f773_terseLabel_en-US" xlink:label="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Garfield PG JV HoldCo LLC</link:label>
    <link:label id="lab_bsprt_GarfieldPGJVHoldCoLLCMember_label_en-US" xlink:label="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Garfield PG JV HoldCo LLC [Member]</link:label>
    <link:label id="lab_bsprt_GarfieldPGJVHoldCoLLCMember_documentation_en-US" xlink:label="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Garfield PG JV HoldCo LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:href="bsprt-20250930.xsd#bsprt_GarfieldPGJVHoldCoLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:to="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_262cde43-3770-4778-b0d6-58574056d7a6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_6d29b301-c033-4320-9d21-a3d9155a8836_terseLabel_en-US" xlink:label="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_label_en-US" xlink:label="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Amortization Expense, after Year Four</link:label>
    <link:label id="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Amortization Expense, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:href="bsprt-20250930.xsd#bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:to="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_8e1df9c9-7db8-4544-a057-22984ea64396_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RiverwalkAkerBSPVentureLLCMember_4dfaea3f-bea9-446b-b71d-b06546c47998_terseLabel_en-US" xlink:label="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Riverwalk Aker BSP Venture LLC</link:label>
    <link:label id="lab_bsprt_RiverwalkAkerBSPVentureLLCMember_label_en-US" xlink:label="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Riverwalk Aker BSP Venture LLC [Member]</link:label>
    <link:label id="lab_bsprt_RiverwalkAkerBSPVentureLLCMember_documentation_en-US" xlink:label="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Riverwalk Aker BSP Venture LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:href="bsprt-20250930.xsd#bsprt_RiverwalkAkerBSPVentureLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:to="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AcquisitionExpensesMember_b5f1abb2-4c66-4a6b-8311-c85c5eed5491_terseLabel_en-US" xlink:label="lab_bsprt_AcquisitionExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition expenses</link:label>
    <link:label id="lab_bsprt_AcquisitionExpensesMember_label_en-US" xlink:label="lab_bsprt_AcquisitionExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquisition Expenses [Member]</link:label>
    <link:label id="lab_bsprt_AcquisitionExpensesMember_documentation_en-US" xlink:label="lab_bsprt_AcquisitionExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AcquisitionExpensesMember" xlink:href="bsprt-20250930.xsd#bsprt_AcquisitionExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AcquisitionExpensesMember" xlink:to="lab_bsprt_AcquisitionExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_a287d288-3196-4ab2-88b8-297889ea8fd6_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Lease Payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_fd54fa90-c976-49ce-8e93-bca82577d41c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in net unrealized gain/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale_ce8c064c-9e7d-4bfb-a7de-295e3bd6e425_terseLabel_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property transferred from real estate owned, held for investment to real estate owned, held for sale</link:label>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale_label_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Transferred From Real Estate Owned, Held-for-Investment To Real Estate Owned, Held-for-Sale</link:label>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale_documentation_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property Transferred From Real Estate Owned, Held-for-Investment To Real Estate Owned, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:to="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MideastMember_17afbe77-02d2-49db-80b9-4d1c919b4e82_terseLabel_en-US" xlink:label="lab_bsprt_MideastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mideast</link:label>
    <link:label id="lab_bsprt_MideastMember_label_en-US" xlink:label="lab_bsprt_MideastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mideast [Member]</link:label>
    <link:label id="lab_bsprt_MideastMember_documentation_en-US" xlink:label="lab_bsprt_MideastMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mideast</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MideastMember" xlink:href="bsprt-20250930.xsd#bsprt_MideastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MideastMember" xlink:to="lab_bsprt_MideastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_6508243e-b5a2-4c7d-9a8a-d0d88ad58fc9_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_fab781f3-d7f1-40bd-84e1-1721b3735b90_netLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total gross carrying value of loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_0690c489-06b1-44d2-a3f6-36f62ec7676d_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Amortized Cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_12134696-22c8-442b-9da1-a6058972ce33_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit loss</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateSecuritiesMember_57f4caad-8c81-432c-8d87-c1d8e125f1ee_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - real estate securities</link:label>
    <link:label id="lab_bsprt_RealEstateSecuritiesMember_label_en-US" xlink:label="lab_bsprt_RealEstateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Securities [Member]</link:label>
    <link:label id="lab_bsprt_RealEstateSecuritiesMember_documentation_en-US" xlink:label="lab_bsprt_RealEstateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateSecuritiesMember" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateSecuritiesMember" xlink:to="lab_bsprt_RealEstateSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset_813e149b-18fe-48d2-bd83-7b05f67da892_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan repurchase option asset</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Loan Repurchase Option Asset</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Loan Repurchase Option Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_d79fc53d-d7e3-441a-b549-182400b508a4_verboseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_3729d99c-7747-4618-9abf-e5e15fec5eae_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_32ca540b-0927-41b4-8fdb-a28478237ef3_totalLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, net amount of liabilities presented on the balance sheet</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchase"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_64ea16ac-f7d6-4315-b4f9-c5495bed34d6_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized Gain/(Loss)</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AgencyMember_799a2b59-b418-412d-b4f4-eb8fa5f7b926_terseLabel_en-US" xlink:label="lab_bsprt_AgencyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency</link:label>
    <link:label id="lab_bsprt_AgencyMember_label_en-US" xlink:label="lab_bsprt_AgencyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agency [Member]</link:label>
    <link:label id="lab_bsprt_AgencyMember_documentation_en-US" xlink:label="lab_bsprt_AgencyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AgencyMember" xlink:href="bsprt-20250930.xsd#bsprt_AgencyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AgencyMember" xlink:to="lab_bsprt_AgencyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered_158a777b-fec4-40ba-b9e1-c1b5db538ba6_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing agreement</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Net Reported Amount, Covered</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered" xlink:to="lab_us-gaap_LoansAndLeasesReceivableNetReportedAmountCovered" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member_285bac73-1126-4aa4-bc9c-0750ea92f9d2_terseLabel_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Note I</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member_label_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note I, Maturing October 2035 [Member]</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member_documentation_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note I, Maturing October 2035</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:href="bsprt-20250930.xsd#bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:to="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PNCWHLineOfCreditMember_56f6e237-4d07-4cab-9f55-28317ba1c48b_terseLabel_en-US" xlink:label="lab_bsprt_PNCWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PNC WH Line of Credit</link:label>
    <link:label id="lab_bsprt_PNCWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_PNCWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PNC WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_PNCWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_PNCWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PNC WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PNCWHLineOfCreditMember" xlink:href="bsprt-20250930.xsd#bsprt_PNCWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PNCWHLineOfCreditMember" xlink:to="lab_bsprt_PNCWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_1cf3861a-5083-45e3-85c6-fb216bd0e685_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductInformationLineItems_09200be3-62a5-4467-afca-b1cbb4bb351b_terseLabel_en-US" xlink:label="lab_us-gaap_ProductInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_ProductInformationLineItems_label_en-US" xlink:label="lab_us-gaap_ProductInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProductInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductInformationLineItems" xlink:to="lab_us-gaap_ProductInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery_00471099-241d-477b-9403-8060190179b0_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage impairment insurance</link:label>
    <link:label id="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery_6f0f9d25-d890-4720-b345-c99d815266d5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">MSR impairment</link:label>
    <link:label id="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery_label_en-US" xlink:label="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights (MSR) Impairment (Recovery)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageServicingRightsMSRImpairmentRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:to="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_2e6131cf-aaf2-41c2-9b08-a5f9f46a6626_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_2a2aabe4-6964-451f-97e3-652af936b380_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk</link:label>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeographicConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeographicConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeographicConcentrationRiskMember" xlink:to="lab_us-gaap_GeographicConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FairValueInputsYield_3698a3a1-f033-4b1e-98be-348cf38bdb35_terseLabel_en-US" xlink:label="lab_bsprt_FairValueInputsYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Yield (percentage)</link:label>
    <link:label id="lab_bsprt_FairValueInputsYield_label_en-US" xlink:label="lab_bsprt_FairValueInputsYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Yield</link:label>
    <link:label id="lab_bsprt_FairValueInputsYield_documentation_en-US" xlink:label="lab_bsprt_FairValueInputsYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FairValueInputsYield" xlink:href="bsprt-20250930.xsd#bsprt_FairValueInputsYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FairValueInputsYield" xlink:to="lab_bsprt_FairValueInputsYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary_1cbf9ff8-384b-4dd0-97ef-f05f636752eb_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate_44a39300-e4e6-4358-ae68-f15126ce6349_terseLabel_en-US" xlink:label="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company holds common units, membership interest, rate</link:label>
    <link:label id="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate_label_en-US" xlink:label="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Holds Common Units, Membership Interest, Rate</link:label>
    <link:label id="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate_documentation_en-US" xlink:label="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Company Holds Common Units, Membership Interest, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:href="bsprt-20250930.xsd#bsprt_CompanyHoldsCommonUnitsMembershipInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:to="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent_d2633f57-6dc2-4dd5-a62f-3caed27ab008_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accounts Payable and Accrued Expenses, Current</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accounts Payable and Accrued Expenses, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_d694c7bd-4443-4459-8b07-a1dd36593743_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_93f6e5d3-db69-4b86-a9a8-384c1a37455c_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_f8a7a965-f720-4fce-a74c-0a00ff871993_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash_6bb935f3-eea1-4664-83ba-7496f84cbfac_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, gross amounts not offset on the balance sheet, cash collateral</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NoteOnNoteFinancingMember_3f246915-d874-4645-848b-50bb4bb01344_terseLabel_en-US" xlink:label="lab_bsprt_NoteOnNoteFinancingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financings</link:label>
    <link:label id="lab_bsprt_NoteOnNoteFinancingMember_label_en-US" xlink:label="lab_bsprt_NoteOnNoteFinancingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Note-on-Note Financing [Member]</link:label>
    <link:label id="lab_bsprt_NoteOnNoteFinancingMember_documentation_en-US" xlink:label="lab_bsprt_NoteOnNoteFinancingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Note-on-Note Financing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NoteOnNoteFinancingMember" xlink:href="bsprt-20250930.xsd#bsprt_NoteOnNoteFinancingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NoteOnNoteFinancingMember" xlink:to="lab_bsprt_NoteOnNoteFinancingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock_9ad09b37-4541-444b-94e7-3ca60e091a1b_terseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loans, Held for Sale, Measured at Fair Value</link:label>
    <link:label id="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock_label_en-US" xlink:label="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans, Held for Sale, Measured at Fair Value [Text Block]</link:label>
    <link:label id="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans, Held for Sale, Measured at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:to="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_1e99dfff-f822-421b-947d-7820585a9aec_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost by Year of Origination</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, by Origination Year [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_2bb45a6a-8042-401e-a935-4f4efbcc38d5_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned, held for sale</link:label>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_ac648037-3742-4dd0-9842-7304c269d252_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets, Net</link:label>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_label_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateHeldforsale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateHeldforsale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateHeldforsale" xlink:to="lab_us-gaap_RealEstateHeldforsale" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_72977ed0-8d32-4b22-b254-42fbb195b43b_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfFinancingAgreements_d3df0b3b-4afe-47ff-a827-ae8ff69fc140_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of note-on-note financings</link:label>
    <link:label id="lab_bsprt_NumberOfFinancingAgreements_label_en-US" xlink:label="lab_bsprt_NumberOfFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Financing Agreements</link:label>
    <link:label id="lab_bsprt_NumberOfFinancingAgreements_documentation_en-US" xlink:label="lab_bsprt_NumberOfFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Financing Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfFinancingAgreements" xlink:href="bsprt-20250930.xsd#bsprt_NumberOfFinancingAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfFinancingAgreements" xlink:to="lab_bsprt_NumberOfFinancingAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_f883f618-3e84-4f86-ac5e-ef3bd954bca3_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_3dabbe27-59fa-4893-b370-aa4c3e672801_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy_3132386a-b675-47b6-aa0a-ad0f70a84051_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans</link:label>
    <link:label id="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLoansAndLeasesReceivablePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:to="lab_us-gaap_FinanceLoansAndLeasesReceivablePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_c5fef1c8-4966-403a-aa56-6e2cf1e6696e_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating and Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing_25017485-a96e-44e0-ac20-c5882168f654_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for loss sharing</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Allowance for Loss Sharing</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Allowance for Loss Sharing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_875e3fba-9af7-4f82-b93e-ce94558edb4f_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract_6f5d6909-595d-471e-aaa3-5ca4cd5b137c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_cfedee01-02cb-47ce-97b3-4eadb5779b2f_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
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    <link:label id="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_9ab30eb6-74e9-4d5e-9531-337678e12d0e_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total redeemable convertible preferred stock</link:label>
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    <link:label id="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_label_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock, Nonredeemable or Redeemable, Issuer Option, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue"/>
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    <link:label id="lab_us-gaap_ConvertiblePreferredStockMember_470e6a9d-91c7-4be6-8fd0-62468c2d0a33_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertiblePreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertiblePreferredStockMember" xlink:to="lab_us-gaap_ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_98895a2a-60a1-497b-a315-8761082221ff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loans Receivable by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfessionalFees_1914ad37-2f7b-4a60-91ac-c55797a6c655_terseLabel_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional fees</link:label>
    <link:label id="lab_us-gaap_ProfessionalFees_label_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfessionalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfessionalFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfessionalFees" xlink:to="lab_us-gaap_ProfessionalFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_1ecedf48-5934-4e38-9cfb-8e7d31f0d1c1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, measured at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_ee209908-82ee-46f5-81eb-7aab2d490700_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Treasury notes</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_f4c4e88f-c923-4a0f-abe1-ec9442377f2e_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PeriodOfLoansHeldForSaleSold_ea5944b2-a692-4438-ae9b-d8af5237d1f0_terseLabel_en-US" xlink:label="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period of loans held-for-sale sold</link:label>
    <link:label id="lab_bsprt_PeriodOfLoansHeldForSaleSold_label_en-US" xlink:label="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period of Loans Held-for-Sale Sold</link:label>
    <link:label id="lab_bsprt_PeriodOfLoansHeldForSaleSold_documentation_en-US" xlink:label="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Period of Loans Held-for-Sale Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PeriodOfLoansHeldForSaleSold" xlink:href="bsprt-20250930.xsd#bsprt_PeriodOfLoansHeldForSaleSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PeriodOfLoansHeldForSaleSold" xlink:to="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
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    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember_25ef6af4-8f5e-4955-9153-6f7941412330_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Sale</link:label>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Sale [Member]</link:label>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Sale [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageReceivableHeldForSaleMember" xlink:href="bsprt-20250930.xsd#bsprt_CommercialMortgageReceivableHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageReceivableHeldForSaleMember" xlink:to="lab_bsprt_CommercialMortgageReceivableHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_8c455d17-731e-4b9e-973c-e95bcec6df91_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions from equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentDividendsOrDistributions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:to="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_d6440780-56e1-45c8-8638-7467abbd5edb_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive securities excluded from computation (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
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    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_ec5be219-e30e-45f4-b253-c4f102abcffc_totalLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_c14d5531-c5db-43ca-be70-e4efebeb16d8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_82e0dd24-889c-47e0-b3ff-cd85d7453e18_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Past Due Loans</link:label>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_33a50f6d-1622-4f19-af8c-1a3aa685e918_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_775e80db-6d66-4cef-97fc-f1fdf8b39abd_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in)/provided by financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
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    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
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    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions_2b1bfad8-7ddf-4778-95ec-589cc9481ff3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred fees and other items</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Other Addition</link:label>
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    <link:label id="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation_3785648a-a23f-4c6c-b508-c06511968ff6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation_label_en-US" xlink:label="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateOwnedAccumulatedDepreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:to="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_dbf81e31-9e71-4838-80e1-a3223a71e251_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary_2c29ff2e-1671-4612-a5e6-fd5f6d3f44e0_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR_5741e980-7e0d-4e62-9828-e9acc9473030_terseLabel_en-US" xlink:label="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MSR impairment and amortization</link:label>
    <link:label id="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR_label_en-US" xlink:label="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment And Amortization Of Mortgage Servicing Rights MSR</link:label>
    <link:label id="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR_documentation_en-US" xlink:label="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment And Amortization Of Mortgage Servicing Rights MSR</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:href="bsprt-20250930.xsd#bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:to="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_7991f3a7-61ee-4661-83b4-14a723b9e0a4_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_6398ff97-5201-45db-a7d3-ad3ebbcaed28_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining amount available under share repurchase program</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Remaining Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:to="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockOptionMember_ea4ff3d3-1b22-4457-8c31-41fd795284f6_terseLabel_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options</link:label>
    <link:label id="lab_us-gaap_StockOptionMember_label_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockOptionMember" xlink:to="lab_us-gaap_StockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_0c1e2643-f5c9-47f4-8e43-1766d990e395_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred financing costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementMember_72db9f2b-2ac7-46d4-bb8c-8054bc76eb5d_terseLabel_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MRAs</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementMember_label_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreement [Member]</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementMember_documentation_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MasterRepurchaseAgreementMember" xlink:href="bsprt-20250930.xsd#bsprt_MasterRepurchaseAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MasterRepurchaseAgreementMember" xlink:to="lab_bsprt_MasterRepurchaseAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_520cd599-d41a-4ed8-94c9-e4a612c7aef7_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes_e1cbe8d4-63c9-4893-bfea-dca886fae691_terseLabel_en-US" xlink:label="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reduced the facility capacity</link:label>
    <link:label id="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes_label_en-US" xlink:label="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity to Secure Retail Notes</link:label>
    <link:label id="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes_documentation_en-US" xlink:label="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity to Secure Retail Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes" xlink:href="bsprt-20250930.xsd#bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes" xlink:to="lab_bsprt_LineOfCreditFacilityMaximumBorrowingCapacityToSecureRetailNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_2f7af997-bfc4-4ce1-b871-a5b437f5a943_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted Cash Flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_d02f11c3-f94f-4c8c-9d0d-7abe40ee4e40_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Collateralized Loan Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_TypeOfAgreementAxis_fce0f154-7929-408e-bf59-cc800e67cc50_terseLabel_en-US" xlink:label="lab_bsprt_TypeOfAgreementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Type Of Agreement [Axis]</link:label>
    <link:label id="lab_bsprt_TypeOfAgreementAxis_label_en-US" xlink:label="lab_bsprt_TypeOfAgreementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Type Of Agreement [Axis]</link:label>
    <link:label id="lab_bsprt_TypeOfAgreementAxis_documentation_en-US" xlink:label="lab_bsprt_TypeOfAgreementAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Type Of Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_TypeOfAgreementAxis" xlink:href="bsprt-20250930.xsd#bsprt_TypeOfAgreementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_TypeOfAgreementAxis" xlink:to="lab_bsprt_TypeOfAgreementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_d784ce37-ef8d-4a73-8b26-dd8a9be5093f_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of real estate properties</link:label>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_label_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Real Estate Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfRealEstateProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfRealEstateProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfRealEstateProperties" xlink:to="lab_us-gaap_NumberOfRealEstateProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_690918dd-d99a-46ba-a538-eea5dbc8cb35_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_92423756-3d72-4680-b304-2643b52a11b7_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining lease term (in year)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialMortgageBackedSecuritiesMember_eb61bbee-5815-4768-bb5f-e7e8d883d197_verboseLabel_en-US" xlink:label="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - commercial mortgage loans</link:label>
    <link:label id="lab_us-gaap_CommercialMortgageBackedSecuritiesMember_05c151a9-0265-41dc-a6e5-ba3153d91137_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, commercial mortgage loans</link:label>
    <link:label id="lab_us-gaap_CommercialMortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialMortgageBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:to="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_bb286ea4-ec70-4b00-9488-de3d8e836574_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill &amp; Other Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralWithRightMember_f3b095f2-b6a5-4c36-9279-63cfac7ee9b7_terseLabel_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralWithRightMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral with Right</link:label>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralWithRightMember_label_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralWithRightMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral with Right [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralWithRightMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetPledgedAsCollateralWithRightMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetPledgedAsCollateralWithRightMember" xlink:to="lab_us-gaap_AssetPledgedAsCollateralWithRightMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve_7c4879f2-92cc-40cb-9f49-57c7f3cf9644_terseLabel_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance, Specific Reserve</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve_label_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance, Specific Reserve</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve_documentation_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance, Specific Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:href="bsprt-20250930.xsd#bsprt_LossSharingObligationsAllowanceSpecificReserve"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:to="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_b55e1f74-0170-4d8e-ad03-fa2b5ca6e820_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGoodwillTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract_8f466c61-8df2-479e-8dd5-6de30fd51be5_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Securities Sold under Agreements to Repurchase [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:to="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_d80d3531-a79a-4a66-8b44-904486e502c8_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rental income</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_f7e28c90-8b62-4c69-9787-3006d80e8ddc_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_c8bf892c-2cc6-435e-8a0b-5c230dcf4b95_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_2432fcc8-a6d4-4178-8b98-891dd2a2145d_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesEPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesEPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesEPreferredStockMember" xlink:to="lab_us-gaap_SeriesEPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_7a1af3b7-34a0-4d6b-b342-4c9e6179aac7_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireFinanceReceivables_e6fa2c11-9f25-4d5d-8fd5-a9a1855eaf9b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Origination and purchase of commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireFinanceReceivables_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Finance Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireFinanceReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:to="lab_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseIncome_263c1b37-1064-4fb8-b289-1cb558ab4a50_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from real estate owned</link:label>
    <link:label id="lab_us-gaap_LeaseIncome_label_en-US" xlink:label="lab_us-gaap_LeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseIncome" xlink:to="lab_us-gaap_LeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock_91cb4e63-1969-46b5-bcee-9f8488f6521e_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Owned, Held For Sale</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Sale [Table Text Block]</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateOwnedHeldForSaleTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:to="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth_a25d44c2-872a-4404-9d4a-a15e64e6a3f6_terseLabel_en-US" xlink:label="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum allowable share conversions per month (in shares)</link:label>
    <link:label id="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth_label_en-US" xlink:label="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities, Maximum Allowed Share Conversions Per Month</link:label>
    <link:label id="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth_documentation_en-US" xlink:label="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities, Maximum Allowed Share Conversions Per Month</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:href="bsprt-20250930.xsd#bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:to="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_fa38d2dd-59cc-4d76-a746-2da57f6982ca_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NewEnglandMember_b431b143-03ed-4441-84cf-ca7e88c81599_terseLabel_en-US" xlink:label="lab_bsprt_NewEnglandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New England</link:label>
    <link:label id="lab_bsprt_NewEnglandMember_label_en-US" xlink:label="lab_bsprt_NewEnglandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New England [Member]</link:label>
    <link:label id="lab_bsprt_NewEnglandMember_documentation_en-US" xlink:label="lab_bsprt_NewEnglandMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New England</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NewEnglandMember" xlink:href="bsprt-20250930.xsd#bsprt_NewEnglandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NewEnglandMember" xlink:to="lab_bsprt_NewEnglandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RetailSiteMember_78148055-17b1-41ea-9349-9d2ffb71e108_terseLabel_en-US" xlink:label="lab_srt_RetailSiteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retail</link:label>
    <link:label id="lab_srt_RetailSiteMember_label_en-US" xlink:label="lab_srt_RetailSiteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retail Site [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RetailSiteMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RetailSiteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RetailSiteMember" xlink:to="lab_srt_RetailSiteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GSEMember_32ba7d4e-7b36-4be7-99c7-32243a2f6270_terseLabel_en-US" xlink:label="lab_bsprt_GSEMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value - Agency</link:label>
    <link:label id="lab_bsprt_GSEMember_label_en-US" xlink:label="lab_bsprt_GSEMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GSE [Member]</link:label>
    <link:label id="lab_bsprt_GSEMember_documentation_en-US" xlink:label="lab_bsprt_GSEMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GSE</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GSEMember" xlink:href="bsprt-20250930.xsd#bsprt_GSEMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GSEMember" xlink:to="lab_bsprt_GSEMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MixedUseMember_4a09adca-e9a3-4d79-a4a3-05dc87a5ece1_terseLabel_en-US" xlink:label="lab_bsprt_MixedUseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mixed Use</link:label>
    <link:label id="lab_bsprt_MixedUseMember_label_en-US" xlink:label="lab_bsprt_MixedUseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mixed Use [Member]</link:label>
    <link:label id="lab_bsprt_MixedUseMember_documentation_en-US" xlink:label="lab_bsprt_MixedUseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mixed Use [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MixedUseMember" xlink:href="bsprt-20250930.xsd#bsprt_MixedUseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MixedUseMember" xlink:to="lab_bsprt_MixedUseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GeneralReserveMember_55af7c3d-936e-45bf-981f-5192de369cce_terseLabel_en-US" xlink:label="lab_bsprt_GeneralReserveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General Reserve</link:label>
    <link:label id="lab_bsprt_GeneralReserveMember_label_en-US" xlink:label="lab_bsprt_GeneralReserveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General Reserve [Member]</link:label>
    <link:label id="lab_bsprt_GeneralReserveMember_documentation_en-US" xlink:label="lab_bsprt_GeneralReserveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">General Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GeneralReserveMember" xlink:href="bsprt-20250930.xsd#bsprt_GeneralReserveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GeneralReserveMember" xlink:to="lab_bsprt_GeneralReserveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_88a52839-f068-4822-91e3-bab576ecfa41_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repo and revolving credit facilities, commercial mortgage loans, capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan_44257290-2851-4157-8f32-57304953fe2c_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued under dividend reinvestment plan (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgingPurposeAxis_42bc9e54-70f1-40bf-9115-b6883483c434_terseLabel_en-US" xlink:label="lab_us-gaap_PledgingPurposeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Axis]</link:label>
    <link:label id="lab_us-gaap_PledgingPurposeAxis_label_en-US" xlink:label="lab_us-gaap_PledgingPurposeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PledgingPurposeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgingPurposeAxis" xlink:to="lab_us-gaap_PledgingPurposeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_b895cbb6-c195-4080-93d6-efeca697af11_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common stock repurchases (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_20d7854a-fbb1-46d9-af44-50e898bc0f6c_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_02fbe32f-336d-4d13-8d4b-34f050ebd890_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_5aa1ad3b-0a05-41a7-8c64-73e22299c301_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_04972c38-1e3e-4d56-ae1c-1573e484d9c8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOff_aa3352fe-b61c-4122-b9a2-915258963520_terseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Charge offs from specific allowance for credit losses</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOff_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-Off</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOff_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansOnRealEstateChargeOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:to="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SoutheastMember_cc6a93bf-4b8a-4e60-a1af-2d5fe22c5dfc_terseLabel_en-US" xlink:label="lab_bsprt_SoutheastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Southeast</link:label>
    <link:label id="lab_bsprt_SoutheastMember_label_en-US" xlink:label="lab_bsprt_SoutheastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Southeast [Member]</link:label>
    <link:label id="lab_bsprt_SoutheastMember_documentation_en-US" xlink:label="lab_bsprt_SoutheastMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Southeast</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SoutheastMember" xlink:href="bsprt-20250930.xsd#bsprt_SoutheastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SoutheastMember" xlink:to="lab_bsprt_SoutheastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation_febe6e33-5038-4171-8193-7712450e28a8_terseLabel_en-US" xlink:label="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Granted, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:to="lab_us-gaap_StockGrantedDuringPeriodValueSharebasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_7f5a9cb7-5b92-43b9-9d8f-f5611be60c0d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities_4386e054-5cb1-4f8f-ac2b-c5e78b24d5b1_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, gross amounts not offset on the balance sheet, financial instruments</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_e8c2dacf-7e05-48ed-ab7f-9604ab3ff21d_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_7e8adfb1-20f9-43a3-9c71-91426b27a70c_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_ef1125bb-ccb7-4c8e-ba45-8114c35a0295_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NewPointHoldingsJVLLCMember_fa700c74-7f6e-4f37-918e-9b966a04feb7_terseLabel_en-US" xlink:label="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NewPoint Holdings JV LLC</link:label>
    <link:label id="lab_bsprt_NewPointHoldingsJVLLCMember_label_en-US" xlink:label="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NewPoint Holdings JV LLC [Member]</link:label>
    <link:label id="lab_bsprt_NewPointHoldingsJVLLCMember_documentation_en-US" xlink:label="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NewPoint Holdings JV LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NewPointHoldingsJVLLCMember" xlink:href="bsprt-20250930.xsd#bsprt_NewPointHoldingsJVLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NewPointHoldingsJVLLCMember" xlink:to="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_bd185109-70fd-4bf9-bbd1-87ed3d270516_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PayOffsMortgageServicingRightsMSRs_c63bc62e-aa33-458c-a85d-4c1a5910f6cf_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">MSR payoffs</link:label>
    <link:label id="lab_bsprt_PayOffsMortgageServicingRightsMSRs_label_en-US" xlink:label="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay Offs Mortgage Servicing Rights MSRs</link:label>
    <link:label id="lab_bsprt_PayOffsMortgageServicingRightsMSRs_documentation_en-US" xlink:label="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pay Offs Mortgage Servicing Rights MSRs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:href="bsprt-20250930.xsd#bsprt_PayOffsMortgageServicingRightsMSRs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:to="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_34cbc4ac-bd7f-472c-996f-5969ae2d4851_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent_9840fd30-0a56-4b72-aceb-c40a00c99ccd_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio_204ef4ef-7bf9-4917-bd50-a0c1be2e9702_terseLabel_en-US" xlink:label="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UPB</link:label>
    <link:label id="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio_label_en-US" xlink:label="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-in-Portfolio, Principal Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:to="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_54ba2921-a758-4585-ac5d-b5c057379684_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net change in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_f5fb711c-6092-44cf-9876-b359306138df_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common dividends paid (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JPMRepoFacilityMember_238f41ea-56f5-4c2f-9afe-46938b6ca880_terseLabel_en-US" xlink:label="lab_bsprt_JPMRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JPM Repo Facility</link:label>
    <link:label id="lab_bsprt_JPMRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_JPMRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">JPM Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_JPMRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_JPMRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">JPM Repo Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JPMRepoFacilityMember" xlink:href="bsprt-20250930.xsd#bsprt_JPMRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JPMRepoFacilityMember" xlink:to="lab_bsprt_JPMRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_e845030c-125f-4c13-8763-85d52ad983e1_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain/(Loss) from Investments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:to="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified_b29608a3-6667-4a64-b58e-0fa0f41b21c5_terseLabel_en-US" xlink:label="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and accounts payable - reclassified to other liabilities</link:label>
    <link:label id="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified_label_en-US" xlink:label="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Expenses And Accounts Payable, Reclassified</link:label>
    <link:label id="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified_documentation_en-US" xlink:label="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Expenses And Accounts Payable, Reclassified</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AccruedExpensesAndAccountsPayableReclassified" xlink:href="bsprt-20250930.xsd#bsprt_AccruedExpensesAndAccountsPayableReclassified"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AccruedExpensesAndAccountsPayableReclassified" xlink:to="lab_bsprt_AccruedExpensesAndAccountsPayableReclassified" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_9977ffab-d8cc-4d5b-b284-67ed868201a4_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOffs_f81176b8-a286-4970-934a-fe76664fd1d8_negatedTerseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Principal charge-off</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOffs_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-offs</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOffs_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-offs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansOnRealEstateChargeOffs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:to="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_fcd1e98d-877d-4daf-adcb-5ba7b77fcf9c_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour_66f0749d-fdce-4c2b-b312-5c61ba115347_terseLabel_en-US" xlink:label="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029 and beyond</link:label>
    <link:label id="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour_label_en-US" xlink:label="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, after Year Four and After Year Four</link:label>
    <link:label id="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year Four and After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:href="bsprt-20250930.xsd#bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:to="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_0000c89f-a26f-437d-85e6-691d337d747f_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_575e915d-4e3b-4dd7-909a-964a8033bf28_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_5d8fd4ff-11b6-4c0a-82b6-235f1bfa719e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost basis</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_d6ef6a14-f967-403e-921a-8dfddc6c24c5_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_7218172a-91ad-4fa4-9854-32e3b8d4cc98_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 (Three Months Ended December 31, 2025)</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
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    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_ee9cbf1e-d091-4f77-b176-72fceb2acf21_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Gross (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsGrossExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_c88b9a2a-6df0-4bf0-bbca-2551e996c340_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateNamePropertyTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:to="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_3074d3bf-3549-46ff-b2c5-cc728fb5ab6e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_84c38dad-57cf-4915-ad66-18de637a38d3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, expected tax deductible</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Goodwill, Expected Tax Deductible, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueDomain_ae487a81-56dc-4dcf-aebc-5ec5a15f8a54_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_ae21be93-5045-4a82-9a96-114ce565cc69_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments of deferred financing costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Financing Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfFinancingCosts" xlink:to="lab_us-gaap_PaymentsOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_d63c66f2-8f4f-4cc7-9248-e2a7ecb2ef71_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) from equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_fd30e29a-adfe-4e9a-95ea-f0d1c3679bc3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) from equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BarclaysCapitalIncMember_c7de4cbf-143c-48b8-a208-ec6c5872d3b8_terseLabel_en-US" xlink:label="lab_bsprt_BarclaysCapitalIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barclays Capital Inc.</link:label>
    <link:label id="lab_bsprt_BarclaysCapitalIncMember_label_en-US" xlink:label="lab_bsprt_BarclaysCapitalIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barclays Capital Inc [Member]</link:label>
    <link:label id="lab_bsprt_BarclaysCapitalIncMember_documentation_en-US" xlink:label="lab_bsprt_BarclaysCapitalIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barclays Capital Inc [Member]</link:label>
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    <link:label id="lab_bsprt_ServicingFeePayablePolicyTextBlock_55b8314c-2162-40f0-a4aa-8aed6c012e9a_terseLabel_en-US" xlink:label="lab_bsprt_ServicingFeePayablePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Fee Payable</link:label>
    <link:label id="lab_bsprt_ServicingFeePayablePolicyTextBlock_label_en-US" xlink:label="lab_bsprt_ServicingFeePayablePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fee Payable [Policy Text Block]</link:label>
    <link:label id="lab_bsprt_ServicingFeePayablePolicyTextBlock_documentation_en-US" xlink:label="lab_bsprt_ServicingFeePayablePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fee Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ServicingFeePayablePolicyTextBlock" xlink:href="bsprt-20250930.xsd#bsprt_ServicingFeePayablePolicyTextBlock"/>
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    <link:label id="lab_us-gaap_LeasesAbstract_fb980436-76fb-4d44-b7fe-73f813b1e303_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeasesAbstract"/>
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    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds_7600500e-339d-4913-b79f-5f09b0648b1c_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Bonds</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Number of Bonds</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Number of Bonds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:href="bsprt-20250930.xsd#bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet_51c9076a-fc51-4a22-a1bf-05c4ff40b39b_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights, net</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgage Servicing Rights, Net</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgage Servicing Rights, Net</link:label>
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    <link:label id="lab_us-gaap_CompensatedAbsencesPolicy_cb302714-b232-4e6c-ba4a-eadfd0fa23f2_terseLabel_en-US" xlink:label="lab_us-gaap_CompensatedAbsencesPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Compensation Plans (Nonqualified)</link:label>
    <link:label id="lab_us-gaap_CompensatedAbsencesPolicy_label_en-US" xlink:label="lab_us-gaap_CompensatedAbsencesPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensated Absences Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensatedAbsencesPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CompensatedAbsencesPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensatedAbsencesPolicy" xlink:to="lab_us-gaap_CompensatedAbsencesPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_4a7ca9a3-5a7d-4061-b740-b26798dcc015_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Four</link:label>
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    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_66f15144-6e50-4343-8cd6-35cea3ed6098_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaterized loan obligation</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts and Financing Receivables [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
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    <link:label id="lab_us-gaap_LossContingencyAccrualRollForward_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyAccrualRollForward"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
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    <link:label id="lab_bsprt_U.S.BankNationalAssociationMember_6aa333af-4f7c-40b6-ac05-c92b67a8f346_terseLabel_en-US" xlink:label="lab_bsprt_U.S.BankNationalAssociationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Bank National Association</link:label>
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    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_7e7105ed-fa45-4cc5-bc1c-2db09d072a0f_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
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    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_ca71e827-9c7d-4d9e-b401-e4bb5db017b8_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financings</link:label>
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    <link:label id="lab_us-gaap_SecuredDebt_label_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
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    <link:label id="lab_bsprt_RealEstateOwnedDepreciation_c1d92e36-1f18-488a-8be8-c3bb40a57265_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedDepreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedDepreciation_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Depreciation</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedDepreciation_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedDepreciation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedDepreciation" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateOwnedDepreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedDepreciation" xlink:to="lab_bsprt_RealEstateOwnedDepreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_2da01748-0ef7-4f6f-a1a1-7034d8c6e058_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingDerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:to="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember_bf966dcb-598c-4059-ab8e-eac5c91fe8d5_terseLabel_en-US" xlink:label="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee to Acquire and Originate Real Estate Debt</link:label>
    <link:label id="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember_label_en-US" xlink:label="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee to Acquire and Originate Real Estate Debt [Member]</link:label>
    <link:label id="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember_documentation_en-US" xlink:label="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fee to Acquire and Originate Real Estate Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:href="bsprt-20250930.xsd#bsprt_FeetoAcquireandOriginateRealEstateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:to="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_504bd25d-9e9c-4a2f-bc9b-4e8d8b3ebdee_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ThirdPartyVendorAgreementMember_d3f79e47-3e9c-45b3-bfbd-d87d93a8c5fb_terseLabel_en-US" xlink:label="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third Party Vendor Agreement</link:label>
    <link:label id="lab_bsprt_ThirdPartyVendorAgreementMember_label_en-US" xlink:label="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Vendor Agreement [Member]</link:label>
    <link:label id="lab_bsprt_ThirdPartyVendorAgreementMember_documentation_en-US" xlink:label="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Vendor Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ThirdPartyVendorAgreementMember" xlink:href="bsprt-20250930.xsd#bsprt_ThirdPartyVendorAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ThirdPartyVendorAgreementMember" xlink:to="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_954e1075-18bc-41c3-8a7f-004770a3bca5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Security Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeCollateralObligationToReturnSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_8dfe22e1-3f0b-4244-830e-bcc4dff14007_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset_73d89376-63c2-4840-9efd-f8ecc2691ab9_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, gross amounts offset on the balance sheet</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_3b7f7924-77ac-4998-9739-66e00b7f4534_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_021bb968-1f53-478b-a2bf-5b83123a9478_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_e19c9d08-b0d4-4f32-a666-d058a1221ca9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_465401b1-c43e-4552-957d-36dc6136db93_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year one, originated in current fiscal year</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_4a3d059a-eca0-458e-a5e4-0c9b6e951cdb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_dc31ac26-a44c-481d-9108-2e127f56eea4_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:to="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_30740f03-b5c4-46fe-b0a2-58811a7a05a6_netLabel_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_2069ddeb-bdf3-416d-8a8b-592a72aeba64_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale</link:label>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_e4821e63-0366-4c25-a7fd-ca72ed2d2682_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value - non-Agency</link:label>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_label_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageReceivablesMember" xlink:to="lab_us-gaap_MortgageReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProfessionalFeeMember_3f13abdb-0eb5-4243-9bbb-1149261e7719_terseLabel_en-US" xlink:label="lab_bsprt_ProfessionalFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional Fee</link:label>
    <link:label id="lab_bsprt_ProfessionalFeeMember_label_en-US" xlink:label="lab_bsprt_ProfessionalFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Fee [Member]</link:label>
    <link:label id="lab_bsprt_ProfessionalFeeMember_documentation_en-US" xlink:label="lab_bsprt_ProfessionalFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Professional Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProfessionalFeeMember" xlink:href="bsprt-20250930.xsd#bsprt_ProfessionalFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProfessionalFeeMember" xlink:to="lab_bsprt_ProfessionalFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_7c1c172b-25b9-4fcf-ae40-d3d8eceb2a0d_totalLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total future minimum rent</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_6a1791b7-0c03-480a-9289-5c3f160f0bca_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">90 or more days past due</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_3e10d8c0-0217-43c7-a07f-567d7fbfc123_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_58432029-e22e-4cec-8ef3-9470949c92e4_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, at fair value</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_bb6cc5ed-477f-48bc-9a39-8f888484fb2b_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityLenderDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:to="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_7c8c37de-ba22-4123-ba66-6f1fcdbc3488_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_ac5b2f32-d822-4ac7-8cf7-68146b3f87a3_totalLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities, at fair value</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_b4fee5fd-3388-4a49-aed8-62de9a991630_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_8b83ac2b-64c8-4db1-8b38-3670dc2fbb29_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_3e0da301-6840-46ef-bdd2-332bf413cf4d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery_6861b26c-e714-48b6-bee2-40d0c7f6864a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Charge offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff (Recovery)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal_d216ef1b-00ba-4088-955d-4b91bdb7a479_negatedLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Principal repayments</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Collections of Principal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateCollectionsOfPrincipal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:to="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_9ee54419-c7de-4862-8e84-a3b68f82da77_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_92ef013d-0620-415b-bd14-814619c46d96_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_feef7ced-f544-4063-a844-91dd4ba00d7a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year three, originated in prior fiscal year two</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_4af6385f-307b-491f-b468-88feef25ccba_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_1aa29911-2a07-4f47-a08a-753ff725e50c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SalesOfPledgedInvestmentSecurities_c3ca499c-c710-41be-b08d-e91f686b54c7_terseLabel_en-US" xlink:label="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales of investment securities, held to maturity</link:label>
    <link:label id="lab_bsprt_SalesOfPledgedInvestmentSecurities_label_en-US" xlink:label="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales Of Pledged Investment Securities</link:label>
    <link:label id="lab_bsprt_SalesOfPledgedInvestmentSecurities_documentation_en-US" xlink:label="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sales Of Pledged Investment Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SalesOfPledgedInvestmentSecurities" xlink:href="bsprt-20250930.xsd#bsprt_SalesOfPledgedInvestmentSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SalesOfPledgedInvestmentSecurities" xlink:to="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_a80b528e-35a6-456c-aa95-ee9a7b33c33c_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income/(loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans_d7ec1e44-a45c-4bec-903e-3adea7abbad6_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Repurchase Agreements Commercial Mortgage Loans</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Repurchase Agreements Commercial Mortgage Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm_70e6dfea-a830-4f4c-a9d4-18366cae15eb_terseLabel_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Master repurchase agreements maturity (days)</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm_label_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreements, Maturity Term</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm_documentation_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreements, Maturity Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:href="bsprt-20250930.xsd#bsprt_MasterRepurchaseAgreementsMaturityTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:to="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_c6c58a2f-8da6-48b0-a343-fc5907a4cfa5_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_0901d6e2-4580-4c32-b059-81cc55518aa0_terseLabel_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management and subordinated performance fee</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_b55591de-22b0-47f7-bbcf-5734ee0496af_verboseLabel_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset management and subordinated performance fee</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_label_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management And Subordinated Performance Fees</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_documentation_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management And Subordinated Performance Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:href="bsprt-20250930.xsd#bsprt_AssetManagementAndSubordinatedPerformanceFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:to="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_f4c810bd-b158-4b39-9bd8-711d1c66ad6f_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DenominatorAbstract_c9400349-efac-48f4-9e51-d55f27c1ad7e_terseLabel_en-US" xlink:label="lab_bsprt_DenominatorAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator</link:label>
    <link:label id="lab_bsprt_DenominatorAbstract_label_en-US" xlink:label="lab_bsprt_DenominatorAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Denominator [Abstract]</link:label>
    <link:label id="lab_bsprt_DenominatorAbstract_documentation_en-US" xlink:label="lab_bsprt_DenominatorAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Denominator [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DenominatorAbstract" xlink:href="bsprt-20250930.xsd#bsprt_DenominatorAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DenominatorAbstract" xlink:to="lab_bsprt_DenominatorAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_3ebe05a6-d4a3-48f1-8331-324fac868a3f_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt, amount outstanding</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_293c9aba-4e61-4fc3-adfd-9ff3be35e2fa_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding principal</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_0f6dbf42-65fe-44e2-8841-94caff0bd9d9_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_6ef7d672-d3a4-413a-8d75-10e94d0cdec0_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WeightedAverageRiskRatingOfLoans_f69200e6-3bc7-4eca-875b-22beb7ae2de3_terseLabel_en-US" xlink:label="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average risk rating of loans</link:label>
    <link:label id="lab_bsprt_WeightedAverageRiskRatingOfLoans_label_en-US" xlink:label="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Risk Rating Of Loans</link:label>
    <link:label id="lab_bsprt_WeightedAverageRiskRatingOfLoans_documentation_en-US" xlink:label="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Risk Rating of Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WeightedAverageRiskRatingOfLoans" xlink:href="bsprt-20250930.xsd#bsprt_WeightedAverageRiskRatingOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WeightedAverageRiskRatingOfLoans" xlink:to="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure_b72366b8-9643-4c61-992f-ecbf980c73d7_terseLabel_en-US" xlink:label="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain/(loss) on derivatives and Realized gain/(loss) on derivatives</link:label>
    <link:label id="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure_label_en-US" xlink:label="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Sale Of Mortgage Loans, Fair Value Disclosure</link:label>
    <link:label id="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure_documentation_en-US" xlink:label="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Sale Of Mortgage Loans, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:href="bsprt-20250930.xsd#bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:to="lab_bsprt_UnrealizedGainLossOnSaleOfMortgageLoansFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_54c6d861-a824-4f06-ba76-0ca26c73b29a_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FranklinBSPRealtyTrustIncMember_72297357-826b-48ba-85fb-10f1e5c822e9_terseLabel_en-US" xlink:label="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Franklin BSP Realty Trust, Inc</link:label>
    <link:label id="lab_bsprt_FranklinBSPRealtyTrustIncMember_label_en-US" xlink:label="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Franklin BSP Realty Trust, Inc [Member]</link:label>
    <link:label id="lab_bsprt_FranklinBSPRealtyTrustIncMember_documentation_en-US" xlink:label="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Franklin BSP Realty Trust, Inc</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FranklinBSPRealtyTrustIncMember" xlink:href="bsprt-20250930.xsd#bsprt_FranklinBSPRealtyTrustIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FranklinBSPRealtyTrustIncMember" xlink:to="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateTable_f2a67868-9746-4642-aac5-9ea483017842_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:label id="lab_us-gaap_RealEstateTable_label_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateTable" xlink:to="lab_us-gaap_RealEstateTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_401bf467-a838-46d6-8bdf-30b8fadee1cd_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableRecordedInvestmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums_d553fba4-0c07-4ae9-bdf3-17461f3a3525_negatedTerseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization/accretion of fees and other items</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Accretion (Amortization) Of Discounts And Premiums</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Accretion (Amortization) of Discounts and Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:to="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_3e4de37c-cd57-4e93-81d2-04f80b2508d5_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_d73fc1a8-0575-4592-8f40-c3d8b2d357d4_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_0d0d1b17-68c2-4cec-93e1-d0b0705cd617_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for Credit Losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ForwardSaleCommitmentsMember_ed35d4b7-528c-411c-b5b9-6a901833521c_terseLabel_en-US" xlink:label="lab_bsprt_ForwardSaleCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale commitments</link:label>
    <link:label id="lab_bsprt_ForwardSaleCommitmentsMember_label_en-US" xlink:label="lab_bsprt_ForwardSaleCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Sale Commitments [Member]</link:label>
    <link:label id="lab_bsprt_ForwardSaleCommitmentsMember_documentation_en-US" xlink:label="lab_bsprt_ForwardSaleCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Sale Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ForwardSaleCommitmentsMember" xlink:href="bsprt-20250930.xsd#bsprt_ForwardSaleCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ForwardSaleCommitmentsMember" xlink:to="lab_bsprt_ForwardSaleCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecurities_b4f1387f-efe7-4f2e-8a6f-c808e3e8bca0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral Pledged</link:label>
    <link:label id="lab_us-gaap_DebtSecurities_label_en-US" xlink:label="lab_us-gaap_DebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecurities" xlink:to="lab_us-gaap_DebtSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_f6a8e520-049a-4402-b650-a69fdd18e030_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember_f7308861-e44e-4ba7-822f-bd324688e938_terseLabel_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Eliminated in Consolidation</link:label>
    <link:label id="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember_label_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Eliminated in Consolidation [Member]</link:label>
    <link:label id="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember_documentation_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Eliminated in Consolidation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:href="bsprt-20250930.xsd#bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:to="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_dc2a3e48-cd6b-47b6-a52b-92b1225e8fb5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other segment items</link:label>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_label_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingOtherItemAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:to="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_dd6a76c3-6a7a-499d-9a49-214545a14865_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average useful economic useful life</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_ab2a0087-2ca8-4787-ae2e-f43da7871337_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_c1aeb83a-24b5-4d1f-8f88-6da0d7cba355_terseLabel_en-US" xlink:label="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and beyond</link:label>
    <link:label id="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_label_en-US" xlink:label="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Four</link:label>
    <link:label id="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:href="bsprt-20250930.xsd#bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:to="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet_221a2c2f-09a3-4a4f-a24f-74915f118bb8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accretion of deferred commitment fees</link:label>
    <link:label id="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet_label_en-US" xlink:label="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Deferred Loan Origination Fees, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfDeferredLoanOriginationFeesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:to="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_ef4db6ca-42ff-4dfc-be0d-1871698c9ee4_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_42c2543e-9c6c-45f5-b1cb-806a34c6de70_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment_2c53c696-24e4-4a78-a43d-04d3a4b7de4b_terseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment_label_en-US" xlink:label="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Commercial Mortgage Loans Held-For-Investment</link:label>
    <link:label id="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Commercial Mortgage Loans Held-For-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:href="bsprt-20250930.xsd#bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:to="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_65acb0fc-215f-43e2-bc94-23d3d8e6355e_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividends declared (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_88e394e8-a3d6-4286-a14a-bebd2946935f_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_002292bc-76b3-41b9-b457-b0953c94bba5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_c66ada4e-3259-4e03-9a52-c114ab50657d_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets acquired</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets"/>
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    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossSharingObligationsPercent" xlink:href="bsprt-20250930.xsd#bsprt_LossSharingObligationsPercent"/>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_057fb3fc-a8ea-4219-ac5c-8967d2313ad9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level II</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_2e7cb4f8-5f74-4b95-bb22-1800cd78ee0f_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments"/>
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    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_e84fa6fa-0dc5-4ea6-82e9-481e77394f78_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_173294d3-d417-497d-8dda-2c627465d49f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_940ad3c0-aa45-4a3b-9cf4-cf91059162fd_terseLabel_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetPledgedAsCollateralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:to="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_5def8105-4ad9-43ec-95b7-f6e67f364713_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoMember"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_5b22dd85-b14a-401c-9c06-e3023d797fb4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers into Level III</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_6465a0b0-0b88-4ea1-b96d-ae92a8bcefc8_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Secured Debt</link:label>
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    <link:label id="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount_e0a48c6b-8b09-4933-a408-3c3e9d4e0517_terseLabel_en-US" xlink:label="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing and ancillary fees</link:label>
    <link:label id="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount_label_en-US" xlink:label="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ancillary Fee Income Generated by Servicing Financial Assets, Amount</link:label>
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    <link:label id="lab_bsprt_InvestmentSecuritiesHeldToMaturityPolicyTextBlock_187bd7a0-ba2d-4373-8d92-0b2c0f7ebc99_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentSecuritiesHeldToMaturityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Securities Held to Maturity</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_45ce3238-934e-4bc8-9c67-0a3dbb865910_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_97568add-c245-462f-8c1c-3376d0a7f8ca_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, beginning of period</link:label>
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    <link:label id="lab_us-gaap_DerivativeAssets_216c843b-b18f-42e0-9374-f1a7c4c667c2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, measured at fair value</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_f356eac2-e684-4bd7-a78f-c93442748396_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Nonrecurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Nonrecurring [Member]</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_8306c9c1-5aa5-47ff-aa66-129faef17789_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Interest Payable, Net</link:label>
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    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_f7a5ea08-4ce3-4dca-9699-3204197f1437_totalLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill)</link:label>
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    <link:label id="lab_srt_ProductsAndServicesDomain_24f45351-e88a-4530-82e0-ccbe32e497eb_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_be7b3784-b9d7-4563-a01f-639715914095_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerConcentrationRiskMember" xlink:to="lab_us-gaap_CustomerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_6ecc6e74-2fd7-4b06-8b6b-21f10c2e9a60_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ParentMember"/>
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    <link:label id="lab_us-gaap_ProfitLoss_2ee5cc4d-6675-4053-ad99-531f77353a27_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_2a20c119-4de5-40eb-9e8c-e34ff4b171bd_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_3ded62be-cae5-4886-b748-37e679f597b4_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Three</link:label>
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    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_87e032dd-07f3-48be-a6eb-ea7634e51399_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_9c870420-7bc3-4ac8-8248-f92937702141_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue_0eeb786a-b05d-4804-80c2-d454344e66db_terseLabel_en-US" xlink:label="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan commitments and forward sale commitments, net</link:label>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_1462470b-04eb-4bf7-9afb-1901fb0c6d06_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
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    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_07f8a521-4d1b-4f46-855c-e57bfd5c9612_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series H Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series H Preferred Stock [Member]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_e3796760-e28e-45c6-96f4-e3f8a7f6d8f1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allocation of the Purchase Consideration</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList_628538d6-59b8-4b01-90f0-84f997abd731_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
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    <link:label id="lab_dei_CityAreaCode_2b3322d4-df53-4323-8cde-6617d83900d9_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
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    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_90b79eeb-6fd1-4131-880c-a09527cdd490_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Allowance for Credit Losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgagesMember_5b9bd85a-ff9d-429a-8d2b-d99cec3b29b9_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage note payable</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_33c4369c-804f-4b1e-9c36-f629989e232f_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_label_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgages [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesMember" xlink:to="lab_us-gaap_MortgagesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_e57cb832-d1a2-4ebf-b75f-e00ddb34c2d6_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_df4bdc66-cd6e-400e-8d73-a85419240cbf_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative services expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_c595c4cf-3c11-4b78-9fe2-22c673ddb315_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Administrative services expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_1b680506-f092-4f41-b1ca-b2ba23f6aaff_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_a76b0f03-4d9d-479b-82bf-962fb6950df3_netLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_d153da82-c5da-4370-817d-45119266428c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_e0a58959-9437-4a97-88a8-61c3c857e464_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net lease cost</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_3750eadf-869b-4126-927e-4f76ce1949e6_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Payables due to affiliate</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_2364157f-2ae5-42f7-9562-be76f90039c9_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_ae5689af-fbca-4800-9645-f92ebbe4fbb0_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at December 31, 2024</link:label>
    <link:label id="lab_us-gaap_Goodwill_dbbb8632-361a-48f1-8cc6-b4a206806606_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at September 30, 2025</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyEstimateOfPossibleLoss_42f707e3-6fba-4da5-927c-49d2b986688b_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing under the DUS program</link:label>
    <link:label id="lab_us-gaap_LossContingencyEstimateOfPossibleLoss_label_en-US" xlink:label="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Estimate of Possible Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyEstimateOfPossibleLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:to="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_ad5f47bd-9310-497d-b18c-b6ad6beb48c3_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageServicingRightsPolicyTextBlock_6ad4baaa-daad-4f9e-beb1-9f28ba514552_terseLabel_en-US" xlink:label="lab_bsprt_MortgageServicingRightsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights, net</link:label>
    <link:label id="lab_bsprt_MortgageServicingRightsPolicyTextBlock_label_en-US" xlink:label="lab_bsprt_MortgageServicingRightsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights [Policy Text Block]</link:label>
    <link:label id="lab_bsprt_MortgageServicingRightsPolicyTextBlock_documentation_en-US" xlink:label="lab_bsprt_MortgageServicingRightsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageServicingRightsPolicyTextBlock" xlink:href="bsprt-20250930.xsd#bsprt_MortgageServicingRightsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageServicingRightsPolicyTextBlock" xlink:to="lab_bsprt_MortgageServicingRightsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinanceLeaseLiabilityHeldForSale_ad3c2650-c95b-4ad1-a5c5-03508b454358_terseLabel_en-US" xlink:label="lab_bsprt_FinanceLeaseLiabilityHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible lease liability, held for sale - reclassified to other liabilities</link:label>
    <link:label id="lab_bsprt_FinanceLeaseLiabilityHeldForSale_label_en-US" xlink:label="lab_bsprt_FinanceLeaseLiabilityHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Held for Sale</link:label>
    <link:label id="lab_bsprt_FinanceLeaseLiabilityHeldForSale_documentation_en-US" xlink:label="lab_bsprt_FinanceLeaseLiabilityHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Held for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinanceLeaseLiabilityHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_FinanceLeaseLiabilityHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinanceLeaseLiabilityHeldForSale" xlink:to="lab_bsprt_FinanceLeaseLiabilityHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForLossSharing_e596e5b4-2b69-48b8-a07a-9cf340870f62_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for loss sharing</link:label>
    <link:label id="lab_bsprt_AllowanceForLossSharing_label_en-US" xlink:label="lab_bsprt_AllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance For Loss Sharing</link:label>
    <link:label id="lab_bsprt_AllowanceForLossSharing_documentation_en-US" xlink:label="lab_bsprt_AllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance For Loss Sharing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForLossSharing" xlink:href="bsprt-20250930.xsd#bsprt_AllowanceForLossSharing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AllowanceForLossSharing" xlink:to="lab_bsprt_AllowanceForLossSharing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_981fa56e-406b-41aa-9323-55101ca1b86a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers out of Level III</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers out of Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ReserveQuantitiesByTypeOfReserveAxis_d41d52a1-413d-436d-8201-938bc3990aa1_terseLabel_en-US" xlink:label="lab_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Petroleum Reserves [Axis]</link:label>
    <link:label id="lab_srt_ReserveQuantitiesByTypeOfReserveAxis_label_en-US" xlink:label="lab_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Petroleum Reserves [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ReserveQuantitiesByTypeOfReserveAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:to="lab_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OptionMember_7caf0b66-b6bc-467a-bfe9-189adbae588f_terseLabel_en-US" xlink:label="lab_us-gaap_OptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options</link:label>
    <link:label id="lab_us-gaap_OptionMember_label_en-US" xlink:label="lab_us-gaap_OptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Options Held [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OptionMember" xlink:to="lab_us-gaap_OptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NonPerformingFinancialInstrumentsRollForward_2a7ebb6c-8e76-4aaf-a7fb-83fa94eadb7c_terseLabel_en-US" xlink:label="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Performing Financial Instruments [Roll Forward]</link:label>
    <link:label id="lab_bsprt_NonPerformingFinancialInstrumentsRollForward_label_en-US" xlink:label="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Performing Financial Instruments [Roll Forward]</link:label>
    <link:label id="lab_bsprt_NonPerformingFinancialInstrumentsRollForward_documentation_en-US" xlink:label="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Performing Financial Instruments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:href="bsprt-20250930.xsd#bsprt_NonPerformingFinancialInstrumentsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:to="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_01c8f79f-f8ba-410f-becd-f321a2940d51_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_df67af88-c93a-4688-909d-c9e2c22ee823_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Revenue</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing of Financial Assets [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_99b30b23-5b09-49b3-be97-edd487d3e7bd_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_ee0ac78f-83c6-4a1a-89a0-72e7b1dfa8c8_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_92ef50d5-c6cd-4d29-9377-fe87d46c628b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions declared</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditConcentrationRiskMember_4c05f8f3-ca12-4689-a18c-26f82b6816b5_terseLabel_en-US" xlink:label="lab_us-gaap_CreditConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CreditConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CreditConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditConcentrationRiskMember" xlink:to="lab_us-gaap_CreditConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_September2021MortgageNotePayableAffiliateMember_be27697c-78d8-4e82-928e-bac390623ed3_terseLabel_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Affiliate</link:label>
    <link:label id="lab_bsprt_September2021MortgageNotePayableAffiliateMember_label_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Affiliate [Member]</link:label>
    <link:label id="lab_bsprt_September2021MortgageNotePayableAffiliateMember_documentation_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:href="bsprt-20250930.xsd#bsprt_September2021MortgageNotePayableAffiliateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:to="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfDelinquentLoans_f99ceee3-be9d-45aa-9555-02157d670f34_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of delinquent ginnie mae loans</link:label>
    <link:label id="lab_bsprt_NumberOfDelinquentLoans_label_en-US" xlink:label="lab_bsprt_NumberOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Delinquent Loans</link:label>
    <link:label id="lab_bsprt_NumberOfDelinquentLoans_documentation_en-US" xlink:label="lab_bsprt_NumberOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Delinquent Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfDelinquentLoans" xlink:href="bsprt-20250930.xsd#bsprt_NumberOfDelinquentLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfDelinquentLoans" xlink:to="lab_bsprt_NumberOfDelinquentLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_3a2acd1a-ed56-4212-a083-52606d0b3e54_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_012c3ff4-649a-425c-96d8-36d9104c9d21_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_e1757a99-518e-42e3-8efa-69b5ff01e229_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CLO cash held by servicer</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_18959177-76d5-4843-8de3-ec5c497437e3_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_d53e756e-f52f-4195-b86c-a062bb922f88_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeFinanceLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:to="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossStatusAxis_c20f4da0-2b67-4dd5-804a-46f0331c68a6_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditLossStatusAxis_label_en-US" xlink:label="lab_us-gaap_CreditLossStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditLossStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossStatusAxis" xlink:to="lab_us-gaap_CreditLossStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_7508b6b0-24e8-4619-a929-a40dce3096ea_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in)/provided by investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
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    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_InterestPaidNet_973982aa-e292-4814-b022-6559807f3698_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash payments for interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_95b3e831-aa5b-4ec2-834d-300fd2b32cd9_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_694fffba-9c6d-42bf-a93f-fd61426b3bf4_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Accounting</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_a6b22f42-c32e-4f00-97f8-39b7b0bee6b0_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityAxis" xlink:to="lab_us-gaap_LineOfCreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_27bf39bf-563b-44ba-a43c-94703041b16e_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, ROU</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MezzanineLoansMember_b01022c4-7707-47a5-91d6-e6867bcec0f7_terseLabel_en-US" xlink:label="lab_bsprt_MezzanineLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine loans</link:label>
    <link:label id="lab_bsprt_MezzanineLoansMember_label_en-US" xlink:label="lab_bsprt_MezzanineLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mezzanine Loans [Member]</link:label>
    <link:label id="lab_bsprt_MezzanineLoansMember_documentation_en-US" xlink:label="lab_bsprt_MezzanineLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mezzanine Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MezzanineLoansMember" xlink:href="bsprt-20250930.xsd#bsprt_MezzanineLoansMember"/>
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    <link:label id="lab_bsprt_GainLossOnMortgageBankingActivitiesNet_b3c37be6-446b-4044-85e7-fca041065299_negatedTerseLabel_en-US" xlink:label="lab_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Mortgage banking activities</link:label>
    <link:label id="lab_bsprt_GainLossOnMortgageBankingActivitiesNet_label_en-US" xlink:label="lab_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Loss On Mortgage Banking Activities Net</link:label>
    <link:label id="lab_bsprt_GainLossOnMortgageBankingActivitiesNet_documentation_en-US" xlink:label="lab_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain Loss On Mortgage Banking Activities Net</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseCost_3a359247-fe32-44ec-8a10-23a854b0e49c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_41d107e1-72ae-46a9-a3fd-48ceb762857d_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Axis]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis"/>
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    <link:label id="lab_bsprt_LoansTransferredFromCommercialMortgageLoansHeldForInvestmentToCommercialMortgageLoansHeldForSale_5edcef08-79b4-4f59-ab87-93a689775f26_terseLabel_en-US" xlink:label="lab_bsprt_LoansTransferredFromCommercialMortgageLoansHeldForInvestmentToCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans transferred from commercial mortgage loans, held for investment to commercial mortgage loans, held for sale</link:label>
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    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
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    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_4d4697de-353d-4ba4-a460-d326e1eaea61_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition expenses</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition-Related Cost, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAbstract_9a80e9da-f70b-4564-98b9-3f4fd6747976_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:label id="lab_us-gaap_RealEstateAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAbstract" xlink:to="lab_us-gaap_RealEstateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2021FL7Member_545344c1-f933-4c80-8eb1-1d3e7bcf7e28_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2021FL7Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2021-FL7 Issuer</link:label>
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    <link:label id="lab_us-gaap_EquityAbstract_855cf1a2-2aa5-418f-9979-a7d95f960f14_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity:</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock_e8a26ad7-e5d9-4179-bab2-947a424cb634_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Other Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_10a4ac8f-7db5-4acf-9b56-ac3c892132c2_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_49cbf6a5-86f8-452c-8a69-696faaa049cf_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGoodwillTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTable" xlink:to="lab_us-gaap_ScheduleOfGoodwillTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating2Member_1b83fa14-6b22-4342-af2c-53b34b57cb02_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2</link:label>
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    <link:label id="lab_bsprt_InvestmentRating2Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating2Member" xlink:href="bsprt-20250930.xsd#bsprt_InvestmentRating2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating2Member" xlink:to="lab_bsprt_InvestmentRating2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary_03a60c97-b030-4194-bca6-d43c76d94c37_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_8cb785b4-88dc-4531-aeff-cac418801255_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorLoansMember_73f6bfd2-0c00-44f6-885b-19cf98c27066_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior loans</link:label>
    <link:label id="lab_us-gaap_SeniorLoansMember_label_en-US" xlink:label="lab_us-gaap_SeniorLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorLoansMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorLoansMember" xlink:to="lab_us-gaap_SeniorLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_f575cc68-cd63-4029-be5e-9aefc48332a0_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OperatingExpensesAdjusted_ffc60b11-ff5f-4a38-8a00-6aa9ce72a41f_negatedLabel_en-US" xlink:label="lab_bsprt_OperatingExpensesAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_bsprt_OperatingExpensesAdjusted_label_en-US" xlink:label="lab_bsprt_OperatingExpensesAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses, Adjusted</link:label>
    <link:label id="lab_bsprt_OperatingExpensesAdjusted_documentation_en-US" xlink:label="lab_bsprt_OperatingExpensesAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Expenses, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OperatingExpensesAdjusted" xlink:href="bsprt-20250930.xsd#bsprt_OperatingExpensesAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OperatingExpensesAdjusted" xlink:to="lab_bsprt_OperatingExpensesAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_ce0ce214-df3d-4573-b3dd-e41a0bda643a_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther_414d97e8-5b27-411d-bc86-f45dcb0cbfaa_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Other Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements_7f3f0b8a-a1d2-4fae-90cf-46911792e461_terseLabel_en-US" xlink:label="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of repurchase agreements - real estate securities</link:label>
    <link:label id="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements_label_en-US" xlink:label="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Real Estate Security Repurchase Agreements</link:label>
    <link:label id="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements_documentation_en-US" xlink:label="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments for Real Estate Security Repurchase Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements" xlink:href="bsprt-20250930.xsd#bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements" xlink:to="lab_bsprt_PaymentsForRealEstateSecurityRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_cbe84ca5-5e8d-4ee8-a7c6-83dade9378db_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossContingencyAccrualWriteOff_39660c7a-0dd4-4eb0-baa7-ef801bb803b0_terseLabel_en-US" xlink:label="lab_bsprt_LossContingencyAccrualWriteOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Write-offs</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualWriteOff_label_en-US" xlink:label="lab_bsprt_LossContingencyAccrualWriteOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual Write off</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualWriteOff_documentation_en-US" xlink:label="lab_bsprt_LossContingencyAccrualWriteOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual Write off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossContingencyAccrualWriteOff" xlink:href="bsprt-20250930.xsd#bsprt_LossContingencyAccrualWriteOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossContingencyAccrualWriteOff" xlink:to="lab_bsprt_LossContingencyAccrualWriteOff" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_554b2319-2672-4510-bed7-84c909c97e9c_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_492400b3-67bf-4391-8e46-b5254e30ef48_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leases</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_0d364f57-82a2-45a0-9f84-74a4bdd760f6_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_d5703a85-4682-42d2-bc61-a2eef96526dd_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_67dfcc87-674d-402f-850d-2a2ac3cde52f_netLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value - Non-Agency</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:to="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_b0dc2702-cd0d-464b-89f2-5b2149accf53_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common stock repurchases</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_2ffc94ca-9d7d-4d53-97c3-601637dc4058_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Accumulated Other Comprehensive Income/(Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JeffersonvilleJVAffiliateMember_304ce336-8d1d-48a4-bd77-3d61bec27bdc_terseLabel_en-US" xlink:label="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jeffersonville JV, Affiliate</link:label>
    <link:label id="lab_bsprt_JeffersonvilleJVAffiliateMember_label_en-US" xlink:label="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jeffersonville JV, Affiliate [Member]</link:label>
    <link:label id="lab_bsprt_JeffersonvilleJVAffiliateMember_documentation_en-US" xlink:label="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jeffersonville JV, Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JeffersonvilleJVAffiliateMember" xlink:href="bsprt-20250930.xsd#bsprt_JeffersonvilleJVAffiliateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JeffersonvilleJVAffiliateMember" xlink:to="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonperformingFinancingReceivableMember_cdf780d7-9acb-44f9-b525-cfd7465e780e_terseLabel_en-US" xlink:label="lab_us-gaap_NonperformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonperforming Financial Instruments</link:label>
    <link:label id="lab_us-gaap_NonperformingFinancingReceivableMember_label_en-US" xlink:label="lab_us-gaap_NonperformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonperforming Financial Instruments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonperformingFinancingReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonperformingFinancingReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonperformingFinancingReceivableMember" xlink:to="lab_us-gaap_NonperformingFinancingReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_5898ef7d-4cf2-4db3-b663-bac2f18f581f_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_IndustrialPropertyMember_a83de6d2-60bc-4f36-9311-28008334dde4_terseLabel_en-US" xlink:label="lab_srt_IndustrialPropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industrial</link:label>
    <link:label id="lab_srt_IndustrialPropertyMember_label_en-US" xlink:label="lab_srt_IndustrialPropertyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industrial Property [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_IndustrialPropertyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_IndustrialPropertyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_IndustrialPropertyMember" xlink:to="lab_srt_IndustrialPropertyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_d93993a3-d34f-4025-81a5-0ae324efd3a6_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolver Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_3afd1e7a-cf5c-4ca6-86ea-9a7602675aeb_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_b0d5dda9-02a1-454b-a96e-8c2a182bbc7e_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_label_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Credit Derivatives [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCreditDerivativesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCreditDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCreditDerivativesMember" xlink:to="lab_us-gaap_OtherCreditDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_0684e2af-7507-4a63-93ee-9e0bf7c7914b_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Earnings (Loss) since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:to="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans_9396d7cb-c93d-4ae6-ab2e-144d3f0204fd_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions and originations</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, New Mortgage Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoansOnRealEstateNewMortgageLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherGeneralExpense_061a1509-4ae6-4369-adba-7cee0ee10421_terseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralExpense_026b50a5-5839-42c5-977c-3c188ee08efb_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other related party expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherGeneralExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherGeneralExpense" xlink:to="lab_us-gaap_OtherGeneralExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_98970440-86ed-4b84-abf0-02ae22b9cd97_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JeffersonvilleGeorgiaMember_7e29c6eb-b716-46a3-9feb-333c1e58aa84_terseLabel_en-US" xlink:label="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jeffersonville, GA</link:label>
    <link:label id="lab_bsprt_JeffersonvilleGeorgiaMember_label_en-US" xlink:label="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jeffersonville, Georgia [Member]</link:label>
    <link:label id="lab_bsprt_JeffersonvilleGeorgiaMember_documentation_en-US" xlink:label="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jeffersonville, Georgia</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JeffersonvilleGeorgiaMember" xlink:href="bsprt-20250930.xsd#bsprt_JeffersonvilleGeorgiaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JeffersonvilleGeorgiaMember" xlink:to="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation_ce5f6a88-fe1e-4172-a081-f1d48c0f6804_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accrued Compensation</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accrued Compensation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_4fe3c515-23e8-490d-b086-f4362864598d_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PurchaseAndSaleAgreementMember_9cfff9e4-28ce-409d-9326-d99b9fc2adc1_terseLabel_en-US" xlink:label="lab_bsprt_PurchaseAndSaleAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase And Sale Agreement</link:label>
    <link:label id="lab_bsprt_PurchaseAndSaleAgreementMember_label_en-US" xlink:label="lab_bsprt_PurchaseAndSaleAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchase And Sale Agreement [Member]</link:label>
    <link:label id="lab_bsprt_PurchaseAndSaleAgreementMember_documentation_en-US" xlink:label="lab_bsprt_PurchaseAndSaleAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchase And Sale Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PurchaseAndSaleAgreementMember" xlink:href="bsprt-20250930.xsd#bsprt_PurchaseAndSaleAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PurchaseAndSaleAgreementMember" xlink:to="lab_bsprt_PurchaseAndSaleAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtIssuanceCostsAndDiscount_5431995d-be0b-4227-83af-ff4967f31f54_terseLabel_en-US" xlink:label="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing cost and discount</link:label>
    <link:label id="lab_bsprt_DebtIssuanceCostsAndDiscount_label_en-US" xlink:label="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs And Discount</link:label>
    <link:label id="lab_bsprt_DebtIssuanceCostsAndDiscount_documentation_en-US" xlink:label="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs and Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtIssuanceCostsAndDiscount" xlink:href="bsprt-20250930.xsd#bsprt_DebtIssuanceCostsAndDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtIssuanceCostsAndDiscount" xlink:to="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SecuredDebtExcluded_04ceffb7-82d0-409d-87bb-0485b425046e_terseLabel_en-US" xlink:label="lab_bsprt_SecuredDebtExcluded" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligation excluded</link:label>
    <link:label id="lab_bsprt_SecuredDebtExcluded_label_en-US" xlink:label="lab_bsprt_SecuredDebtExcluded" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt Excluded</link:label>
    <link:label id="lab_bsprt_SecuredDebtExcluded_documentation_en-US" xlink:label="lab_bsprt_SecuredDebtExcluded" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Secured Debt Excluded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SecuredDebtExcluded" xlink:href="bsprt-20250930.xsd#bsprt_SecuredDebtExcluded"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SecuredDebtExcluded" xlink:to="lab_bsprt_SecuredDebtExcluded" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PurchasesOfPledgedInvestmentSecurities_0270f119-1b87-4ebb-956f-a58f75d43e63_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investment securities, held to maturity</link:label>
    <link:label id="lab_bsprt_PurchasesOfPledgedInvestmentSecurities_label_en-US" xlink:label="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchases Of Pledged Investment Securities</link:label>
    <link:label id="lab_bsprt_PurchasesOfPledgedInvestmentSecurities_documentation_en-US" xlink:label="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchases Of Pledged Investment Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:href="bsprt-20250930.xsd#bsprt_PurchasesOfPledgedInvestmentSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:to="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FreddieMacMember_21ac6953-8477-45a7-9f59-e172dc753b83_terseLabel_en-US" xlink:label="lab_bsprt_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Freddie Mac</link:label>
    <link:label id="lab_bsprt_FreddieMacMember_label_en-US" xlink:label="lab_bsprt_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Freddie Mac [Member]</link:label>
    <link:label id="lab_bsprt_FreddieMacMember_documentation_en-US" xlink:label="lab_bsprt_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Freddie Mac</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FreddieMacMember" xlink:href="bsprt-20250930.xsd#bsprt_FreddieMacMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FreddieMacMember" xlink:to="lab_bsprt_FreddieMacMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_fde7b2fa-7f46-4c06-bd36-d35dac852084_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
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    <link:label id="lab_bsprt_FurnitureFixturesandEquipmentMember_ecc5fbb6-7ac7-49fb-96bf-b4270c5064ad_terseLabel_en-US" xlink:label="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture, Fixtures and Equipment</link:label>
    <link:label id="lab_bsprt_FurnitureFixturesandEquipmentMember_label_en-US" xlink:label="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture Fixtures and Equipment [Member]</link:label>
    <link:label id="lab_bsprt_FurnitureFixturesandEquipmentMember_documentation_en-US" xlink:label="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Furniture Fixtures and Equipment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FurnitureFixturesandEquipmentMember" xlink:href="bsprt-20250930.xsd#bsprt_FurnitureFixturesandEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FurnitureFixturesandEquipmentMember" xlink:to="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_c90a8d76-a5b2-439f-9d18-82d9feb1afb2_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_7cc44ca1-edc0-4278-9056-bcdf2531b9aa_netLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_cf764b10-d754-46d2-a1b4-8a89533a1e35_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets, at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AtTheMarketSalesAgreementMember_69c8e3c8-f1d9-43b4-9471-2088bf1fe3f4_terseLabel_en-US" xlink:label="lab_bsprt_AtTheMarketSalesAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At The Market Sales Agreement</link:label>
    <link:label id="lab_bsprt_AtTheMarketSalesAgreementMember_label_en-US" xlink:label="lab_bsprt_AtTheMarketSalesAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At The Market Sales Agreement [Member]</link:label>
    <link:label id="lab_bsprt_AtTheMarketSalesAgreementMember_documentation_en-US" xlink:label="lab_bsprt_AtTheMarketSalesAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At The Market Sales Agreement</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_828d7eab-579a-4faa-9fba-be6b36b64107_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on unsecured debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfUnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_bb52551f-bcd5-4a00-a878-2cd949e7e576_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WalgreensJVAffiliateMember_e6874e0e-2e6d-482b-bf06-947dc4bd808c_terseLabel_en-US" xlink:label="lab_bsprt_WalgreensJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Walgreens JV, Affiliate</link:label>
    <link:label id="lab_bsprt_WalgreensJVAffiliateMember_label_en-US" xlink:label="lab_bsprt_WalgreensJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Walgreens JV, Affiliate [Member]</link:label>
    <link:label id="lab_bsprt_WalgreensJVAffiliateMember_documentation_en-US" xlink:label="lab_bsprt_WalgreensJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Walgreens JV, Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WalgreensJVAffiliateMember" xlink:href="bsprt-20250930.xsd#bsprt_WalgreensJVAffiliateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WalgreensJVAffiliateMember" xlink:to="lab_bsprt_WalgreensJVAffiliateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_f9dd1140-48ac-4ac2-a0fa-9e33617e1873_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_f7b4f20e-e38d-4a99-b637-3787ca0cc4df_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_bd639021-7425-48fd-a7b1-11a06f5e1837_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_88b342fe-c51e-4092-bfd2-9b1c8a50ba8e_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember_a19508ef-4cf5-4019-85c6-fb9eeb010992_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans, Held for Investment and Real Estate Securities, Available for Sale</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss and Debt Securities, Available-for-Sale, Excluding Accrued Interest [Member]</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss and Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember" xlink:href="bsprt-20250930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLossAndDebtSecuritiesAvailableForSaleExcludingAccruedInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_46693aeb-da2f-4ebf-b22a-f5088c8d0147_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate, stated percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
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    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_366f8712-2697-40ad-bb56-dea527c5691a_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments_a0fa9b3b-a37e-4396-b08e-729711034037_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments_2938a289-9860-4656-a348-52c4be482951_negatedNetLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Other than Temporary Impairments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:to="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ExitCapitalizationRate_37c892ed-93ec-4c75-95ac-fc1abd12a153_terseLabel_en-US" xlink:label="lab_bsprt_ExitCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit capitalization rate</link:label>
    <link:label id="lab_bsprt_ExitCapitalizationRate_label_en-US" xlink:label="lab_bsprt_ExitCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exit Capitalization Rate</link:label>
    <link:label id="lab_bsprt_ExitCapitalizationRate_documentation_en-US" xlink:label="lab_bsprt_ExitCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exit Capitalization Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ExitCapitalizationRate" xlink:href="bsprt-20250930.xsd#bsprt_ExitCapitalizationRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ExitCapitalizationRate" xlink:to="lab_bsprt_ExitCapitalizationRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BarclaysRevolverFacilityMember_0cb89597-8577-4a63-9791-707350fa39a3_terseLabel_en-US" xlink:label="lab_bsprt_BarclaysRevolverFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barclays Revolver Facility</link:label>
    <link:label id="lab_bsprt_BarclaysRevolverFacilityMember_label_en-US" xlink:label="lab_bsprt_BarclaysRevolverFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barclays Revolver Facility [Member]</link:label>
    <link:label id="lab_bsprt_BarclaysRevolverFacilityMember_documentation_en-US" xlink:label="lab_bsprt_BarclaysRevolverFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barclays Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BarclaysRevolverFacilityMember" xlink:href="bsprt-20250930.xsd#bsprt_BarclaysRevolverFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BarclaysRevolverFacilityMember" xlink:to="lab_bsprt_BarclaysRevolverFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_18a7d4a6-d201-493b-b055-3b8bd774aa78_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_eb01bdf0-8211-4404-baa5-6d83997c66c9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts of Recognized Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_d43497a5-bb9c-4172-9673-d48cd3103c25_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanCommitmentsMember_c2bd38b3-672f-4d74-bdf4-c22ebfd3775c_terseLabel_en-US" xlink:label="lab_bsprt_LoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan commitments</link:label>
    <link:label id="lab_bsprt_LoanCommitmentsMember_label_en-US" xlink:label="lab_bsprt_LoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan commitments [Member]</link:label>
    <link:label id="lab_bsprt_LoanCommitmentsMember_documentation_en-US" xlink:label="lab_bsprt_LoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanCommitmentsMember" xlink:href="bsprt-20250930.xsd#bsprt_LoanCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanCommitmentsMember" xlink:to="lab_bsprt_LoanCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NonCompeteAgreementsMember_bcad642d-418b-4491-ae1a-9cae782e16c0_terseLabel_en-US" xlink:label="lab_bsprt_NonCompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-compete Agreements</link:label>
    <link:label id="lab_bsprt_NonCompeteAgreementsMember_label_en-US" xlink:label="lab_bsprt_NonCompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non compete Agreements [Member]</link:label>
    <link:label id="lab_bsprt_NonCompeteAgreementsMember_documentation_en-US" xlink:label="lab_bsprt_NonCompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non compete Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NonCompeteAgreementsMember" xlink:href="bsprt-20250930.xsd#bsprt_NonCompeteAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NonCompeteAgreementsMember" xlink:to="lab_bsprt_NonCompeteAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating1Member_204dc0b8-4424-43f5-9d99-31f2f702dbc5_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1</link:label>
    <link:label id="lab_bsprt_InvestmentRating1Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 1 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating1Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating1Member" xlink:href="bsprt-20250930.xsd#bsprt_InvestmentRating1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating1Member" xlink:to="lab_bsprt_InvestmentRating1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember_b80a988f-cad0-481b-9e30-1feade9813b4_terseLabel_en-US" xlink:label="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS Bonds</link:label>
    <link:label id="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember_label_en-US" xlink:label="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Collateralized Loan Obligations [Member]</link:label>
    <link:label id="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember_documentation_en-US" xlink:label="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Collateralized Loan Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:href="bsprt-20250930.xsd#bsprt_CommercialRealEstateCollateralizedLoanObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:to="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_8680632f-4665-48dc-862f-e83f395fd06a_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets, at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ChurchillRepoFacilityMember_2eac5f8e-115c-4964-a24c-7941356f9628_terseLabel_en-US" xlink:label="lab_bsprt_ChurchillRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Churchill Repo Facility(8)</link:label>
    <link:label id="lab_bsprt_ChurchillRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_ChurchillRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Churchill Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_ChurchillRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_ChurchillRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Churchill Repo Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ChurchillRepoFacilityMember" xlink:href="bsprt-20250930.xsd#bsprt_ChurchillRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ChurchillRepoFacilityMember" xlink:to="lab_bsprt_ChurchillRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BridgeMember_b07c1c4f-d0d2-479b-a929-37af33f3f791_terseLabel_en-US" xlink:label="lab_bsprt_BridgeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bridge</link:label>
    <link:label id="lab_bsprt_BridgeMember_label_en-US" xlink:label="lab_bsprt_BridgeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bridge [Member]</link:label>
    <link:label id="lab_bsprt_BridgeMember_documentation_en-US" xlink:label="lab_bsprt_BridgeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bridge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BridgeMember" xlink:href="bsprt-20250930.xsd#bsprt_BridgeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BridgeMember" xlink:to="lab_bsprt_BridgeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale_77398a38-4a3e-4865-b9b7-fac645a2fd2f_negatedTerseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfer to held for sale</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Transfer To Held For Sale</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Transfer To Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansOnRealEstateTransferToHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:to="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_aa38679b-db65-4fbf-8784-dfb92a57f2b9_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_a5a8838b-b391-4b19-891d-aa77dd151bd9_negatedLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Premium amortization and (discount accretion), net</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract_a952836d-0986-452a-a36f-b5d59e879291_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract_label_en-US" xlink:label="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income, Nonoperating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIncomeDisclosureNonoperatingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:to="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_52a429ec-e2f0-4bf3-b8b0-e4fe7760cddf_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL9Member_24fafa50-bd10-4033-bdcc-925f5340bf69_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL9Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022-FL9 Issuer</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL9Member_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL9Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2022-FL9 [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL9Member_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL9Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2022-FL9</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_f820d56d-1e2e-4d0b-b4ab-9cab0cd1fa9d_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
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    <link:label id="lab_bsprt_InvestmentRating3Member_d4bac7ec-6db7-4633-b4c6-afd76d74bf21_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_e5e202f1-705f-4126-a50d-7bc442e2b745_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseDebt_52fa541f-683f-4759-be4c-e836a18deea2_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid on unsecured debt</link:label>
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    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2021FL6Member_7f0b9b7f-b5ff-4ba0-9729-1166887ef01f_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2021FL6Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2021-FL6 Issuer</link:label>
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    <link:label id="lab_us-gaap_MinorityInterestInJointVentures_d44a8292-a3da-4374-bd8e-17ae3d2b11d0_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestInJointVentures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest in joint ventures</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_4f1c2018-0492-47f0-b5b9-84898db5d978_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
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    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_91aae56d-6686-4921-a11d-a2e6a89f82c6_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_14f54d0a-1cef-442e-8fdb-6cc9a7f68e44_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock</link:label>
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    <link:label id="lab_us-gaap_PreferredStockMember_c06b8734-2281-4d00-b758-26ec1bc9aea3_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred E</link:label>
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    <link:label id="lab_bsprt_BAMLWHLineOfCreditMember_0c1740ae-a9f6-4eda-82d5-786000418610_terseLabel_en-US" xlink:label="lab_bsprt_BAMLWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BAML WH Line of Credit</link:label>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements_99b227ef-a604-4a23-accc-45b927a4977c_negatedTerseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net borrowings (paydowns) on repurchase agreements - real estate securities, less than 90 days maturity</link:label>
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    <link:label id="lab_us-gaap_EscrowDeposit_e3b7612e-92b8-4a0e-953d-744f1a396caf_terseLabel_en-US" xlink:label="lab_us-gaap_EscrowDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Escrow deposit</link:label>
    <link:label id="lab_us-gaap_EscrowDeposit_label_en-US" xlink:label="lab_us-gaap_EscrowDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Escrow Deposit</link:label>
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    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral_c527d0ab-4241-45d1-91e6-87f81568b86f_totalLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, net amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral"/>
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    <link:label id="lab_bsprt_SubsidiaryDomain_af383465-6ed6-4453-833e-088f17d48800_terseLabel_en-US" xlink:label="lab_bsprt_SubsidiaryDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary [Domain]</link:label>
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    <link:label id="lab_bsprt_SubsidiaryDomain_documentation_en-US" xlink:label="lab_bsprt_SubsidiaryDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsidiary [Domain]</link:label>
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    <link:label id="lab_us-gaap_SegmentDomain_21b0bd4f-608e-4a0c-8fc4-b5581700ba02_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossStatusDomain_fc7a4e06-0b81-4409-91f2-fc35ac2251a2_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditLossStatusDomain_label_en-US" xlink:label="lab_us-gaap_CreditLossStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditLossStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossStatusDomain" xlink:to="lab_us-gaap_CreditLossStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_db0b8855-4d60-4c01-a04b-2482a528559e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_5e182582-55b1-42fa-a9d0-b6015dd76a95_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Securities</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1cf861d4-71c1-40fe-90c7-bcd1707cb71e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
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    <link:label id="lab_bsprt_AgencyLicenseIntangiblesMember_f6d909fa-1ce1-49b5-9bc1-62dec91c14a6_terseLabel_en-US" xlink:label="lab_bsprt_AgencyLicenseIntangiblesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency License Intangibles</link:label>
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    <link:label id="lab_bsprt_AgencyLicenseIntangiblesMember_documentation_en-US" xlink:label="lab_bsprt_AgencyLicenseIntangiblesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency License Intangibles</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AgencyLicenseIntangiblesMember" xlink:href="bsprt-20250930.xsd#bsprt_AgencyLicenseIntangiblesMember"/>
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    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_eb6401b9-f573-4192-a1ad-39eca1464dfc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
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    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_83ef6e40-e0a2-4a17-b796-b78b70f1ff98_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income/(Loss) for Real Estate Securities, Available for Sale, Measured at Fair Value</link:label>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent [Member]</link:label>
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    <link:label id="lab_us-gaap_RealEstateOwnedTextBlock_ec6a9d13-bc72-4af0-ad5b-b4e2f01f9085_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOwnedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned</link:label>
    <link:label id="lab_us-gaap_RealEstateOwnedTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstateOwnedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Text Block]</link:label>
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    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_1912f520-4da0-43e5-8139-e3002b6a2830_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, gross amounts offset on the balance sheet</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_337ca05a-e4a8-4933-9cf8-a64c81736430_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of real estate securities, available for sale</link:label>
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    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_9d64f01a-d4a7-466f-a00c-cd94b1428374_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_4c018194-bfa7-44d5-9038-c4a560126c95_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.01 par value, 900,000,000 shares authorized, 82,925,055 and 83,066,789 shares issued and outstanding as of September&#160;30, 2025 and December 31, 2024, respectively</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_0c665e93-12e1-41ff-9812-4a9b2626814e_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, net of amortization</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
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    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_4a8c8839-6cda-4368-b4c0-f915f8602bb6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Participating securities' share in earnings</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_92580f91-a897-4f43-9683-c6aea6417e94_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
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    <link:label id="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1_1075ace3-b092-4cfe-8d86-bb3970a65feb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ChangeInUnrealizedGainLossOnFairValueHedgingInstruments1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Gain)/loss from derivative instruments, net</link:label>
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    <link:label id="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent_a9749663-b8e0-4481-bed8-a0fdbbdc8679_terseLabel_en-US" xlink:label="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advance rate of mortgage loan (percent)</link:label>
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    <link:label id="lab_bsprt_SecuritizationsNotesMember_documentation_en-US" xlink:label="lab_bsprt_SecuritizationsNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Securitization&#8217;s Notes</link:label>
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    <link:label id="lab_bsprt_BenefitStreetPartnersLLCMember_57037a61-4d16-4db1-aa86-4546795cd3f7_terseLabel_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefit Street Partners LLC</link:label>
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    <link:label id="lab_bsprt_BenefitStreetPartnersLLCMember_documentation_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Benefit Street Partners LLC [Member]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_76e21ce1-2339-4f0b-80de-0d391ec86420_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
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    <link:label id="lab_bsprt_DerivativeLiabilitesMember_3f61b2f1-d4b7-499f-91dd-eb8fde27e3cf_terseLabel_en-US" xlink:label="lab_bsprt_DerivativeLiabilitesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilites</link:label>
    <link:label id="lab_bsprt_DerivativeLiabilitesMember_label_en-US" xlink:label="lab_bsprt_DerivativeLiabilitesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative liabilites [Member]</link:label>
    <link:label id="lab_bsprt_DerivativeLiabilitesMember_documentation_en-US" xlink:label="lab_bsprt_DerivativeLiabilitesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative liabilites</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DerivativeLiabilitesMember" xlink:href="bsprt-20250930.xsd#bsprt_DerivativeLiabilitesMember"/>
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    <link:label id="lab_us-gaap_OtherLongTermDebt_9c740add-8a06-435f-9108-1d374f1d2b06_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financings</link:label>
    <link:label id="lab_us-gaap_OtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_OtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLongTermDebt" xlink:to="lab_us-gaap_OtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_a16b5deb-0ee3-4aaa-a0f1-33b8b3cf4154_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Controlling Interest</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember_7943b0ab-3172-41a7-b0fa-0a7ad7468dd9_terseLabel_en-US" xlink:label="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Agency loans</link:label>
    <link:label id="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember_label_en-US" xlink:label="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non US Government Sponsored-Enterprise Insured Loans [Member]</link:label>
    <link:label id="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember_documentation_en-US" xlink:label="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non US Government Sponsored-Enterprise Insured Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:href="bsprt-20250930.xsd#bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:to="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PresentValueDiscountRatePercentage_98085265-8b6c-40b0-8334-ae4af04a04ea_terseLabel_en-US" xlink:label="lab_bsprt_PresentValueDiscountRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value, discount rate, percentage</link:label>
    <link:label id="lab_bsprt_PresentValueDiscountRatePercentage_label_en-US" xlink:label="lab_bsprt_PresentValueDiscountRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Present Value, Discount Rate, Percentage</link:label>
    <link:label id="lab_bsprt_PresentValueDiscountRatePercentage_documentation_en-US" xlink:label="lab_bsprt_PresentValueDiscountRatePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Present Value, Discount Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PresentValueDiscountRatePercentage" xlink:href="bsprt-20250930.xsd#bsprt_PresentValueDiscountRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PresentValueDiscountRatePercentage" xlink:to="lab_bsprt_PresentValueDiscountRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateDebtMember_7b76245b-6539-4394-88cd-451759a06dd7_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Debt and Other Real Estate Investments</link:label>
    <link:label id="lab_bsprt_RealEstateDebtMember_label_en-US" xlink:label="lab_bsprt_RealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Debt [Member]</link:label>
    <link:label id="lab_bsprt_RealEstateDebtMember_documentation_en-US" xlink:label="lab_bsprt_RealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateDebtMember" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateDebtMember" xlink:to="lab_bsprt_RealEstateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member_0e3a836d-408f-41af-bb7c-2a57a4ce0c28_terseLabel_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Note II</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member_label_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note II, Maturing December 2035 [Member]</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member_documentation_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note II, Maturing December 2035</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:href="bsprt-20250930.xsd#bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:to="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_f09a4aa5-d407-4671-880f-ccf511415a39_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_cc85eeaa-52be-4bdf-be1c-85055c83989e_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskLineItems" xlink:to="lab_us-gaap_ConcentrationRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating5Member_8b0dffaf-6a58-4712-9c92-0e4b08166d2e_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating5Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5</link:label>
    <link:label id="lab_bsprt_InvestmentRating5Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating5Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 5 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating5Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating5Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 5 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating5Member" xlink:href="bsprt-20250930.xsd#bsprt_InvestmentRating5Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating5Member" xlink:to="lab_bsprt_InvestmentRating5Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization_0d9c5215-568a-45b8-b9f3-71444d4f66da_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Intangible Assets, Net of Amortization</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Intangible Assets, Net of Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization" xlink:href="bsprt-20250930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredIntangibleAssetsNetOfAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell_5e15d780-6a8c-4702-a306-d6b080ccc598_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded commitments to fund loans and sell loans</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Commitments to Purchase or Sell</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:to="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest_29d2a318-6cbc-414b-86f6-6b1518df7c51_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) before taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss), Including Portion Attributable to Noncontrolling Interest, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_3c7cd82a-253a-4f23-b250-3b40ac1cb33e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_e0f4b33b-2e6e-4fae-b90d-57c9d86d4c0a_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementScenarioAxis" xlink:to="lab_srt_StatementScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherMember_f06076f7-0d4e-44a4-8f64-6926af38d106_terseLabel_en-US" xlink:label="lab_bsprt_OtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_bsprt_OtherMember_label_en-US" xlink:label="lab_bsprt_OtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other [Member]</link:label>
    <link:label id="lab_bsprt_OtherMember_documentation_en-US" xlink:label="lab_bsprt_OtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OtherMember" xlink:href="bsprt-20250930.xsd#bsprt_OtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OtherMember" xlink:to="lab_bsprt_OtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_CA_48335dab-a9d3-41f4-80b4-25a7670f2d38_terseLabel_en-US" xlink:label="lab_stpr_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">California</link:label>
    <link:label id="lab_stpr_CA_label_en-US" xlink:label="lab_stpr_CA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CALIFORNIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_CA" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_CA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_CA" xlink:to="lab_stpr_CA" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_a85925e6-d28a-4ea3-a446-329476c06096_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentNet_4745accb-ee70-4a75-a4e0-d38f3831b3d4_totalLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned, net</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentNet_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Net</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentNet_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:href="bsprt-20250930.xsd#bsprt_RealEstateOwnedHeldForInvestmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:to="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember_799783d6-43eb-4ca8-b5ce-4f4b5c9d115d_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-FL11 Issuer</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2024-FL11 Issuer [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2024-FL11 Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:href="bsprt-20250930.xsd#bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:to="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_2241e960-da70-40f9-a685-2665875a2fec_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_6aee95ff-8b1a-43f1-b2fd-c4d4d6c1e583_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfLoans_7bb6af12-fce1-4b75-90a2-091f494077cd_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of loans</link:label>
    <link:label id="lab_bsprt_NumberOfLoans_23e826e1-7fc0-4252-baed-1b0b436ec191_verboseLabel_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of Loans</link:label>
    <link:label id="lab_bsprt_NumberOfLoans_label_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Loans</link:label>
    <link:label id="lab_bsprt_NumberOfLoans_documentation_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Mezzanine Loans Funded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfLoans" xlink:href="bsprt-20250930.xsd#bsprt_NumberOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfLoans" xlink:to="lab_bsprt_NumberOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_324cd17e-43d9-430c-a7d6-3a6e640a80e2_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain/(Loss)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_e3fdd8d4-0148-4e83-bec0-dbbc0b98e869_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Due to Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInDueToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:to="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember_dd470329-889b-48a9-8be0-68d03f4492d9_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_27326755-ac24-4a8d-8f37-9af810de1241_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ending Weighted Average Interest Rate</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_a7576b11-fb16-42d3-aaa7-d98ebcaf337f_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Interest Rate</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GinneMaeMember_27192729-df34-4197-898a-9848b096c0ae_terseLabel_en-US" xlink:label="lab_bsprt_GinneMaeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ginnie Mae</link:label>
    <link:label id="lab_bsprt_GinneMaeMember_label_en-US" xlink:label="lab_bsprt_GinneMaeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ginne Mae [Member]</link:label>
    <link:label id="lab_bsprt_GinneMaeMember_documentation_en-US" xlink:label="lab_bsprt_GinneMaeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ginne Mae</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GinneMaeMember" xlink:href="bsprt-20250930.xsd#bsprt_GinneMaeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GinneMaeMember" xlink:to="lab_bsprt_GinneMaeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_df919603-df6c-4cdc-a7e5-e51e660716d1_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of cash, cash equivalents and restricted cash:</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebtCurrent_c4b745fe-54cc-4afc-8d0f-9286bab220fb_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured notes</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebtCurrent_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnsecuredDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebtCurrent" xlink:to="lab_us-gaap_UnsecuredDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract_2ffb1535-d8f7-4eec-80d6-b19730d22f3b_terseLabel_en-US" xlink:label="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock:</link:label>
    <link:label id="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract_label_en-US" xlink:label="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Features of Convertible Preferred Stock [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeaturesOfConvertiblePreferredStockAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:to="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_73ec10cd-6a0f-464a-af51-03bbe9dd0535_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLineItems_9438f3b8-4477-494a-a01c-cd5eb1ee3e28_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Line Items]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLineItems_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems" xlink:to="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_fa9b6911-d14f-4aab-b0d8-ac64aee971e1_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialPortfolioSegmentMember_359067b1-2264-4e7e-8aee-1bbee09eae73_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Portfolio Segment</link:label>
    <link:label id="lab_us-gaap_CommercialPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_CommercialPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialPortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialPortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialPortfolioSegmentMember" xlink:to="lab_us-gaap_CommercialPortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan_fb1c4aed-fa6d-43ad-bbbf-bdf90a82d11f_terseLabel_en-US" xlink:label="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Modification accounted for as repayment and new loan</link:label>
    <link:label id="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan_label_en-US" xlink:label="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Modification Accounted For As Repayment And New Loan</link:label>
    <link:label id="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan_documentation_en-US" xlink:label="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Modification Accounted For As Repayment And New Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:href="bsprt-20250930.xsd#bsprt_ModificationAccountedForAsRepaymentAndNewLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:to="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JPMWHLineOfCreditMember_ecb52d15-4dbe-492a-a156-6211c78a5b7b_terseLabel_en-US" xlink:label="lab_bsprt_JPMWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JPM WH Line of Credit</link:label>
    <link:label id="lab_bsprt_JPMWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_JPMWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">JPM WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_JPMWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_JPMWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">JPM WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JPMWHLineOfCreditMember" xlink:href="bsprt-20250930.xsd#bsprt_JPMWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JPMWHLineOfCreditMember" xlink:to="lab_bsprt_JPMWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_f58688bd-269b-474c-8b88-5313ac932554_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_CO_ddf011c8-6b40-46a4-bf77-5926e802d9c6_terseLabel_en-US" xlink:label="lab_stpr_CO" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denver, CO</link:label>
    <link:label id="lab_stpr_CO_label_en-US" xlink:label="lab_stpr_CO" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">COLORADO</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_CO" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_CO"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_CO" xlink:to="lab_stpr_CO" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionRate_0b546d94-b1af-4cf8-b84d-0325111eb215_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction rate (percent)</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionRate_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionRate" xlink:to="lab_us-gaap_RelatedPartyTransactionRate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_a87eb66d-4259-4a97-bfbd-d68cee7760a3_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forecast</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forecast [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioForecastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioForecastMember" xlink:to="lab_srt_ScenarioForecastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WalgreensJVMember_4ff3d773-8960-428d-83f8-c7e7dee2701d_terseLabel_en-US" xlink:label="lab_bsprt_WalgreensJVMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Walgreens JV</link:label>
    <link:label id="lab_bsprt_WalgreensJVMember_label_en-US" xlink:label="lab_bsprt_WalgreensJVMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Walgreens JV [Member]</link:label>
    <link:label id="lab_bsprt_WalgreensJVMember_documentation_en-US" xlink:label="lab_bsprt_WalgreensJVMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Walgreens JV</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WalgreensJVMember" xlink:href="bsprt-20250930.xsd#bsprt_WalgreensJVMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WalgreensJVMember" xlink:to="lab_bsprt_WalgreensJVMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_9b076707-3917-4534-92ca-b1bdcf5a94e0_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_72ca5f22-816a-49a3-89f6-40f4bc871c86_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_ae9377a2-7d41-416e-9b16-0d8dec260fe1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Provision)/benefit for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_fb8af435-abad-400a-8fb4-f0ed2754606a_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Provision/(benefit) for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_52e87940-795d-43a8-8552-110cbd9a6e29_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Provision)/benefit for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_b3504fdb-0694-4b30-b461-2e4d329ab37c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_1f8603d2-52ab-43d6-bfce-d714eccd8da3_netLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Provision/(Benefit)</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember_091635ee-b465-484e-8005-70272e2e717c_terseLabel_en-US" xlink:label="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency loans</link:label>
    <link:label id="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember_label_en-US" xlink:label="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Sponsored-Enterprise Insured Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:to="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherExpenseMember_7c367b67-3486-4e6f-84d6-f4844a0ebedc_terseLabel_en-US" xlink:label="lab_us-gaap_OtherExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Expense</link:label>
    <link:label id="lab_us-gaap_OtherExpenseMember_label_en-US" xlink:label="lab_us-gaap_OtherExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherExpenseMember" xlink:to="lab_us-gaap_OtherExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_4cf5c82f-d427-4761-9a84-161dcfb785ac_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_1cac4297-b153-4b26-a6c7-966d27128a48_terseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on repurchase agreements and revolving credit facilities - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_label_en-US" xlink:label="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Securities Purchased Under Agreements To Resell, Loans Receivable</link:label>
    <link:label id="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds from Securities Purchased under Agreements to Resell, Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:href="bsprt-20250930.xsd#bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:to="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_b03f01a2-8237-49a3-80c2-f052aede04da_totalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income/(loss)</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_b04b9005-7831-4de3-a361-0814950a1cd2_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest, ownership percentage by parent</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_edc23b92-d9d1-4214-99cb-ed8f650ce41f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions from equity method investments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_label_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution, Return of Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:to="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_HospitalityMember_9c346a38-edfd-477c-94d2-6d661c12d521_terseLabel_en-US" xlink:label="lab_bsprt_HospitalityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hospitality</link:label>
    <link:label id="lab_bsprt_HospitalityMember_label_en-US" xlink:label="lab_bsprt_HospitalityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hospitality [Member]</link:label>
    <link:label id="lab_bsprt_HospitalityMember_documentation_en-US" xlink:label="lab_bsprt_HospitalityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hospitality</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_HospitalityMember" xlink:href="bsprt-20250930.xsd#bsprt_HospitalityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_HospitalityMember" xlink:to="lab_bsprt_HospitalityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_dc980b27-ee6e-4157-b0dc-2973523cadaf_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Specific allowance for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_37627354-8439-4783-a55c-8cd8ca3d6ac6_netLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Specific (provision)/benefit for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_cf3c49e2-3fda-40fa-aa99-5949434e9faa_verboseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Specific Allowance for Credit Losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_label_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Specific [Member]</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_documentation_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Specific</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForCreditLossSpecificMember" xlink:href="bsprt-20250930.xsd#bsprt_AllowanceForCreditLossSpecificMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AllowanceForCreditLossSpecificMember" xlink:to="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements_e8f55dd7-0c8e-453b-94c8-92a699c1a9e2_terseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on repurchase agreements - real estate securities</link:label>
    <link:label id="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements_label_en-US" xlink:label="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Real Estate Security Repurchase Agreements</link:label>
    <link:label id="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Real Estate Security Repurchase Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements" xlink:href="bsprt-20250930.xsd#bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements" xlink:to="lab_bsprt_ProceedsFromRealEstateSecurityRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WellsFargoSecuritiesLLCMember_f203a523-5ba3-45d5-877b-2ab495837864_terseLabel_en-US" xlink:label="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Wells Fargo Securities, LLC</link:label>
    <link:label id="lab_bsprt_WellsFargoSecuritiesLLCMember_label_en-US" xlink:label="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Wells Fargo Securities LLC [Member]</link:label>
    <link:label id="lab_bsprt_WellsFargoSecuritiesLLCMember_documentation_en-US" xlink:label="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Wells Fargo Securities LLC [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WellsFargoSecuritiesLLCMember" xlink:href="bsprt-20250930.xsd#bsprt_WellsFargoSecuritiesLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WellsFargoSecuritiesLLCMember" xlink:to="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SantanderSecuritiesMember_45cbdc71-df2f-41e9-b2b6-cfb64cccb6ff_terseLabel_en-US" xlink:label="lab_bsprt_SantanderSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Santander Securities</link:label>
    <link:label id="lab_bsprt_SantanderSecuritiesMember_label_en-US" xlink:label="lab_bsprt_SantanderSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Santander Securities [Member]</link:label>
    <link:label id="lab_bsprt_SantanderSecuritiesMember_documentation_en-US" xlink:label="lab_bsprt_SantanderSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Santander Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SantanderSecuritiesMember" xlink:href="bsprt-20250930.xsd#bsprt_SantanderSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SantanderSecuritiesMember" xlink:to="lab_bsprt_SantanderSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SpecificReserveMember_c904c55b-84d4-4bff-a2f2-7fca7419711e_terseLabel_en-US" xlink:label="lab_bsprt_SpecificReserveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Specific Reserve</link:label>
    <link:label id="lab_bsprt_SpecificReserveMember_label_en-US" xlink:label="lab_bsprt_SpecificReserveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Specific Reserve [Member]</link:label>
    <link:label id="lab_bsprt_SpecificReserveMember_documentation_en-US" xlink:label="lab_bsprt_SpecificReserveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Specific Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SpecificReserveMember" xlink:href="bsprt-20250930.xsd#bsprt_SpecificReserveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SpecificReserveMember" xlink:to="lab_bsprt_SpecificReserveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FeesPerTheFeeArrangement_28d7ebef-e0cf-4813-93e4-b8c26a038958_terseLabel_en-US" xlink:label="lab_bsprt_FeesPerTheFeeArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fees per the fee arrangement</link:label>
    <link:label id="lab_bsprt_FeesPerTheFeeArrangement_label_en-US" xlink:label="lab_bsprt_FeesPerTheFeeArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fees Per The Fee Arrangement</link:label>
    <link:label id="lab_bsprt_FeesPerTheFeeArrangement_documentation_en-US" xlink:label="lab_bsprt_FeesPerTheFeeArrangement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fees Per The Fee Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FeesPerTheFeeArrangement" xlink:href="bsprt-20250930.xsd#bsprt_FeesPerTheFeeArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FeesPerTheFeeArrangement" xlink:to="lab_bsprt_FeesPerTheFeeArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments_27cf7f08-a390-44a4-91f3-76667edcde35_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments_8cc1910a-02a9-4be4-94ba-c1c3ae7b3c52_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends and Other Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendsAndOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:to="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember_6a370c3c-8719-4fff-8063-fb0a510a7d66_terseLabel_en-US" xlink:label="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DRIP</link:label>
    <link:label id="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember_label_en-US" xlink:label="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Reinvestment And Direct Stock Purchase Plan (DRIP) [Member]</link:label>
    <link:label id="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember_documentation_en-US" xlink:label="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividend Reinvestment And Direct Stock Purchase Plan (DRIP)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:href="bsprt-20250930.xsd#bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:to="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_aacaf80e-87b4-4709-a82e-5f7bccdbe2b9_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockSharesAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockSharesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesAcquired" xlink:to="lab_us-gaap_TreasuryStockSharesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_9c753258-8bc5-4682-8960-5f34af82eaca_terseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual servicing fee</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_4c206f20-db51-4510-ab80-6f623261d2e6_totalLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total servicing revenue, net</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_label_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fee, Late Fee, and Ancillary Fee Earned in Exchange for Servicing Financial Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:to="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure_48e59bec-45e3-4916-9f5b-bbc39e0448cc_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage note payable</link:label>
    <link:label id="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Loaned or Sold under Agreements to Repurchase, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:to="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_e4a2afb7-4414-4b5c-987c-f5665c377d06_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GreatLakesMember_342ceccd-f16d-4dad-a39e-4f69b569691b_terseLabel_en-US" xlink:label="lab_bsprt_GreatLakesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Great Lakes</link:label>
    <link:label id="lab_bsprt_GreatLakesMember_label_en-US" xlink:label="lab_bsprt_GreatLakesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Great Lakes [Member]</link:label>
    <link:label id="lab_bsprt_GreatLakesMember_documentation_en-US" xlink:label="lab_bsprt_GreatLakesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Great Lakes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GreatLakesMember" xlink:href="bsprt-20250930.xsd#bsprt_GreatLakesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GreatLakesMember" xlink:to="lab_bsprt_GreatLakesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_6f51084e-1e7c-483e-b8f7-9753ec2d2b79_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Reclassifications, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ClassAUnitsMember_0983f31f-76e3-417a-b65e-64d7acf5973e_terseLabel_en-US" xlink:label="lab_bsprt_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class A Units</link:label>
    <link:label id="lab_bsprt_ClassAUnitsMember_label_en-US" xlink:label="lab_bsprt_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class A Units [Member]</link:label>
    <link:label id="lab_bsprt_ClassAUnitsMember_documentation_en-US" xlink:label="lab_bsprt_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class A Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ClassAUnitsMember" xlink:href="bsprt-20250930.xsd#bsprt_ClassAUnitsMember"/>
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    <link:label id="lab_bsprt_NetAssetsEquityAttributableToParent_bbce6fe5-8977-4c12-a300-b34007dd6ac5_totalLabel_en-US" xlink:label="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders' equity</link:label>
    <link:label id="lab_bsprt_NetAssetsEquityAttributableToParent_label_en-US" xlink:label="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets, Equity, Attributable to Parent</link:label>
    <link:label id="lab_bsprt_NetAssetsEquityAttributableToParent_documentation_en-US" xlink:label="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Assets, Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NetAssetsEquityAttributableToParent" xlink:href="bsprt-20250930.xsd#bsprt_NetAssetsEquityAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NetAssetsEquityAttributableToParent" xlink:to="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross_c9b2e436-1643-4963-b5e0-0cc553bb7490_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, gross amounts of recognized liabilities</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale_86abd291-52a1-4df8-b7b1-d3759f11a40b_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, Net</link:label>
    <link:label id="lab_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale_label_en-US" xlink:label="lab_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Liabilities Associated with Assets Held for Development and Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale" xlink:to="lab_us-gaap_RealEstateLiabilitiesAssociatedWithAssetsHeldForDevelopmentAndSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1_c09ac393-73ba-451f-810f-05b07419e87e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtAmortizedValueAmortization1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:to="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_c06da3b6-2e67-4710-9aa5-e62dc914ce70_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock and Equity Transactions</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_1bdbaf14-6ebe-4adb-bc8b-d0d69a8ee245_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General allowance for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_8378ffdd-b8d4-4c13-bbf3-66166e6c8ee2_netLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">General (provision)/benefit for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_6cc6e446-e6aa-44fc-8ef3-3ea1fa92839d_verboseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">General Allowance for Credit Losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_label_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, General [Member]</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_documentation_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, General</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForCreditLossGeneralMember" xlink:href="bsprt-20250930.xsd#bsprt_AllowanceForCreditLossGeneralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AllowanceForCreditLossGeneralMember" xlink:to="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_e09f0b58-762b-491c-8146-add63497e937_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment, net of allowance for credit losses of $43,981 and $78,083 as of September&#160;30, 2025 and December&#160;31, 2024, respectively</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_a75c0d9c-6b24-4519-8a25-62f3266fc1fb_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_454fc7d5-b7c4-451e-9dc1-8c9e0bd3499b_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total commercial mortgage loans, held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale_c1f705b9-335b-4dd3-a06a-c4f7ed75d457_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale or repayment of commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale, Loan, Mortgage, Held-for-Sale</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:to="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_f5bacb3a-0b5b-4098-ae23-bea7e86787a4_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_6962b988-8ee3-4f96-b8f7-3f3fbf51af16_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_a37b36c2-427c-4207-90cb-46c1dd7d40c0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_b0c9d483-e609-493c-9190-e016aec42ea1_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain"/>
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    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_94c6392f-158b-4323-9870-95487030cbf5_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investment property, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable_26c8f193-f19e-449f-9637-f21a6d9dac17_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal repayments received on commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Collection of Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromCollectionOfLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:to="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_GA_a2409233-b7ba-4d5f-9acd-4c034aa53937_terseLabel_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GEORGIA</link:label>
    <link:label id="lab_stpr_GA_label_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GEORGIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_GA" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_GA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_GA" xlink:to="lab_stpr_GA" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_08ef625f-2540-47f5-960f-0c9a7ddd498f_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_908c9565-7f43-4c68-8129-afd700530f2c_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_88d95c15-4a40-4842-8f73-c15a9047239b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments for common stock repurchases</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_748cd96d-4d08-4b17-b66b-c25f20b42475_terseLabel_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassifications</link:label>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_label_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification, Comparability Adjustment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_IntangibleLeaseAssetsMember_75902859-e047-4511-a2b3-338b473f6696_terseLabel_en-US" xlink:label="lab_bsprt_IntangibleLeaseAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Lease Assets</link:label>
    <link:label id="lab_bsprt_IntangibleLeaseAssetsMember_label_en-US" xlink:label="lab_bsprt_IntangibleLeaseAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Lease Assets [Member]</link:label>
    <link:label id="lab_bsprt_IntangibleLeaseAssetsMember_documentation_en-US" xlink:label="lab_bsprt_IntangibleLeaseAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Intangible Lease Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_IntangibleLeaseAssetsMember" xlink:href="bsprt-20250930.xsd#bsprt_IntangibleLeaseAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_IntangibleLeaseAssetsMember" xlink:to="lab_bsprt_IntangibleLeaseAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_0b377b57-9e9b-480d-8fac-29744acc11ec_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_FL_a8c07989-61f1-4790-b48f-4e3294f1d188_terseLabel_en-US" xlink:label="lab_stpr_FL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Florida</link:label>
    <link:label id="lab_stpr_FL_label_en-US" xlink:label="lab_stpr_FL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">FLORIDA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_FL" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_FL"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_FL" xlink:to="lab_stpr_FL" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_83321e2e-47be-4f6e-8329-d56aa2f5a7f3_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_8dd91a64-b1c0-4ff3-9d0b-82596dbe6c8e_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet_8a0afd84-cb97-4611-a3e6-67b762fc4cc5_terseLabel_en-US" xlink:label="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recoveries</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet_label_en-US" xlink:label="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual, Recoveries (Charge-offs), Net</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet_documentation_en-US" xlink:label="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual, Recoveries (Charge-offs), Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet" xlink:href="bsprt-20250930.xsd#bsprt_LossContingencyAccrualRecoveriesChargeOffsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet" xlink:to="lab_bsprt_LossContingencyAccrualRecoveriesChargeOffsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_27b62b80-4e50-4b36-817e-f1b1e7936d9a_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FifthThirdLineOfCreditMember_d1be433d-8e70-4434-9c43-bb35ca4a5dec_terseLabel_en-US" xlink:label="lab_bsprt_FifthThirdLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fifth Third Line of Credit</link:label>
    <link:label id="lab_bsprt_FifthThirdLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_FifthThirdLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fifth Third Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_FifthThirdLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_FifthThirdLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fifth Third Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FifthThirdLineOfCreditMember" xlink:href="bsprt-20250930.xsd#bsprt_FifthThirdLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FifthThirdLineOfCreditMember" xlink:to="lab_bsprt_FifthThirdLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AdministrativeServicesExpensesMember_7c3b0f96-f4ff-4f15-a0cd-354abfe324a6_terseLabel_en-US" xlink:label="lab_bsprt_AdministrativeServicesExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative services expenses</link:label>
    <link:label id="lab_bsprt_AdministrativeServicesExpensesMember_label_en-US" xlink:label="lab_bsprt_AdministrativeServicesExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Services Expenses [Member]</link:label>
    <link:label id="lab_bsprt_AdministrativeServicesExpensesMember_documentation_en-US" xlink:label="lab_bsprt_AdministrativeServicesExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administrative Services Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AdministrativeServicesExpensesMember" xlink:href="bsprt-20250930.xsd#bsprt_AdministrativeServicesExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AdministrativeServicesExpensesMember" xlink:to="lab_bsprt_AdministrativeServicesExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate_54b90ccb-307c-4a24-a1d5-4dc109bde87b_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate_label_en-US" xlink:label="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Assets and Servicing Liabilities at Fair Value, Assumptions Used to Estimate Fair Value, Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:to="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure_c2b6e212-ce2a-45ff-939f-1708f4211ba5_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Security, Mortgage-Backed, Held-to-Maturity, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:to="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_86e57fa9-36cb-4668-b4cf-4b2724c5ccd0_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_SalesRevenueNetMember_7408fc03-345d-4a0c-bb41-49fa90ce8565_terseLabel_en-US" xlink:label="lab_us-gaap_SalesRevenueNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Benchmark</link:label>
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    <link:label id="lab_stpr_NJ_3e32046a-e643-4fad-ba79-aa13d0226d04_terseLabel_en-US" xlink:label="lab_stpr_NJ" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Jersey</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_ed693e7d-bbc0-4960-bf92-e77af38b3c66_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Basic and Diluted Earnings Per Share</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract_5991d674-44ac-4632-845f-77eb5f5a089a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amounts related to available for sale real estate securities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_772104ab-84a6-4bdd-bb79-bc0a32738696_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_9bd0f3bc-117b-44e5-87d2-d9d1a5853399_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss_1229bcb6-f3b3-4231-903e-63ed01547271_negatedTerseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized (gain)/loss on sale of available for sale securities, measured at fair value</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Trading, Gain (Loss)</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Trading, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:href="bsprt-20250930.xsd#bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_57146eb7-7231-45ff-97f5-b95e0b916b67_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain/(loss) on real estate securities, available for sale</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_56505c9d-ea58-47e8-9796-601e6cb029ba_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_0b1bb17d-2c09-4ba6-b0f1-921a72a3415f_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BarclaysRepoFacilityMember_3ae9d10e-ac5a-4d55-bbf6-aaa99ff4dbe0_terseLabel_en-US" xlink:label="lab_bsprt_BarclaysRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barclays Repo Facility</link:label>
    <link:label id="lab_bsprt_BarclaysRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_BarclaysRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barclays Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_BarclaysRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_BarclaysRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barclays Repo Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BarclaysRepoFacilityMember" xlink:href="bsprt-20250930.xsd#bsprt_BarclaysRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BarclaysRepoFacilityMember" xlink:to="lab_bsprt_BarclaysRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_e714231d-b797-472e-9548-7c0bfbe1c0ad_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividends_ffc354f3-9894-455b-af6b-b9a5119d1a3b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions paid</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividends" xlink:to="lab_us-gaap_PaymentsOfDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableGainLossOnSalesNet_3d447915-421e-4c3c-aa50-1cffe74e4dc1_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableGainLossOnSalesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Gain (Loss) on Sales, Net</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableGainLossOnSalesNet_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableGainLossOnSalesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Gain (Loss) on Sales, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableGainLossOnSalesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableGainLossOnSalesNet"/>
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    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure_7e8b4ec5-4145-4a38-a0f9-de5ddf49dc73_negatedLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Transfer to real estate owned</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Transfer On Foreclosure</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Transfer on Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:href="bsprt-20250930.xsd#bsprt_MortgageLoansOnRealEstateTransferOnForeclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:to="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_9fca4889-47fb-4437-8fa0-6b76fb4ce07b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts Offset on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_7d7eaa43-1a2d-450c-9252-f4afb6f26006_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingArrLineItems"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_694f13a1-380e-4cfd-957f-cb3c48ec930e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear"/>
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    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_5abbd386-3f32-403d-a325-c04d51e53d2c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember_c5cc2259-4e30-4551-a63b-883d238e8d7e_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Investment</link:label>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Investment [Member]</link:label>
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    <link:label id="lab_us-gaap_Liabilities_c720ea1b-84eb-4635-9c88-6c3a790e7645_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_3855cfd1-a746-4980-afac-7421d3752811_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
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    <link:label id="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease_20dbbf83-8741-46bd-966c-c801f2574a04_terseLabel_en-US" xlink:label="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions/(distributions) in non-controlling interest, net</link:label>
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    <link:label id="lab_us-gaap_ProductConcentrationRiskMember_cbe953ca-6a49-4c81-a8f1-3bf9f8187fae_terseLabel_en-US" xlink:label="lab_us-gaap_ProductConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Concentration Risk</link:label>
    <link:label id="lab_us-gaap_ProductConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_ProductConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProductConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductConcentrationRiskMember" xlink:to="lab_us-gaap_ProductConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValueOutstanding_f379373a-9d04-4d16-b647-02eb5ac6964d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock - at par value</link:label>
    <link:label id="lab_us-gaap_CommonStockValueOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValueOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValueOutstanding"/>
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    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain_5529c564-439a-46dc-859c-0a0554af0248_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument Performance Status [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument Performance Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentPerformanceStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:to="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateAxis_d5a61cff-91b8-4d7f-bb11-d6054da00089_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:label id="lab_us-gaap_VariableRateAxis_label_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateAxis" xlink:to="lab_us-gaap_VariableRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossSharingObligationsAllowance_299baa1c-64a5-48d0-b16a-255c24efe7b9_terseLabel_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing obligations, allowance</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowance_label_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowance_documentation_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossSharingObligationsAllowance" xlink:href="bsprt-20250930.xsd#bsprt_LossSharingObligationsAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossSharingObligationsAllowance" xlink:to="lab_bsprt_LossSharingObligationsAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_eb38a14d-cd64-4b60-abd7-e8e67ed44e50_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_d5a28f76-edae-4014-9e1d-643f1edcd562_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationStateCountryCode"/>
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    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonNeosMember"/>
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