Mortgage Loans Held for Sale and Warehouse Lines of Credit - Schedule of Outstanding Warehouse Lines of Credit (Details) - USD ($)	12 Months Ended
Dec. 31, 2024	Dec. 31, 2023
Short-Term Debt [Line Items]
Facility Size	$ 425,000,000
Warehouse lines of credit	244,070,000	$ 126,218,000
Funding Facility 1 \| Warehouse Agreement Borrowings
Short-Term Debt [Line Items]
Facility Size	100,000,000
Warehouse lines of credit	$ 60,747,000	61,709,000
Variable interest rate (as a percent)	2.125%
Cash collateral deposit	$ 15,000,000.0
Funding Facility 2 \| Warehouse Agreement Borrowings
Short-Term Debt [Line Items]
Facility Size	150,000,000
Warehouse lines of credit	74,472,000	40,088,000
Cash collateral deposit	$ 3,800,000
Funding Facility 2 \| Warehouse Agreement Borrowings \| Minimum
Short-Term Debt [Line Items]
Variable interest rate (as a percent)	2.10%
Funding Facility 2 \| Warehouse Agreement Borrowings \| Maximum
Short-Term Debt [Line Items]
Variable interest rate (as a percent)	2.25%
Funding Facility 3 \| Warehouse Agreement Borrowings
Short-Term Debt [Line Items]
Facility Size	$ 175,000,000
Warehouse lines of credit	108,851,000	$ 24,421,000
Cash collateral deposit	$ 0
Funding Facility 3 \| Warehouse Agreement Borrowings \| Minimum
Short-Term Debt [Line Items]
Variable interest rate (as a percent)	1.75%
Funding Facility 3 \| Warehouse Agreement Borrowings \| Maximum
Short-Term Debt [Line Items]
Variable interest rate (as a percent)	3.75%

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

No definition available.

Name:	us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of cash restricted as to withdrawal or usage, classified as current. Cash includes, but is not limited to, currency on hand, demand deposits with banks or financial institutions, and other accounts with general characteristics of demand deposits.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482913/230-10-50-8

+ Details

Name:	us-gaap_RestrictedCashCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_ShortTermDebtLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying value as of the balance sheet date of the outstanding short-term borrowings under a revolving line of credit used by mortgage bankers to finance the origination or purchase of loans.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

+ Details

Name:	us-gaap_WarehouseAgreementBorrowings
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_DebtInstrumentAxis=aurcu_FundingFacility1DueSeptember302025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ShortTermDebtTypeAxis=us-gaap_WarehouseAgreementBorrowingsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=aurcu_FundingFacility2DueMarch62025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=aurcu_FundingFacility3DueAugust12025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: