Cash Equivalents and Marketable Securities - Contractual Maturities of Marketable Securities at Estimated Fair Value (Details) - USD ($) $ in Thousands	Mar. 31, 2024	Dec. 31, 2023
Cash and Cash Equivalents [Abstract]
Due in one year or less	$ 191,090	$ 115,784
Due in 1 - 2 years	65,999	34,600
Total marketable securities	$ 257,089	$ 150,384

Debt Securities, Available-For-Sale, Fair Value, Maturity, Allocated And Single Maturity Date, After Year One

No definition available.

Name:	syre_DebtSecuritiesAvailableForSaleFairValueMaturityAllocatedAndSingleMaturityDateAfterYearOne
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Fair value of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), with single maturity date and allocated without single maturity date, maturing in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481800/320-10-50-3

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 942
-SubTopic 320
-Name Accounting Standards Codification
-Section 50
-Paragraph 3A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480832/942-320-50-3A

+ Details

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

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481830/320-10-45-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479130/326-30-45-1

+ Details

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

- References

No definition available.

+ Details

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