Leases - Weighted-Average Remaining Lease Term and Discount Rates for Operating and Finance Leases (Details)	Dec. 31, 2023	Dec. 31, 2022
Lease term (years)
Operating leases	0 years	5 years 3 months 18 days
Finance leases	0 years	7 months 6 days
Discount rate
Operating leases	0.00%	10.60%
Finance leases	0.00%	10.20%

Lease, Weighted Average Discount Rate

No definition available.

Name:	syre_LeaseWeightedAverageDiscountRateAbstract
Namespace Prefix:	syre_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Lease, Weighted Average Remaining Lease Term

+ References

No definition available.

+ Details

Name:	syre_LeaseWeightedAverageRemainingLeaseTermAbstract
Namespace Prefix:	syre_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average discount rate for finance lease calculated at point in time.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Weighted average remaining lease term for finance lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Weighted average discount rate for operating lease calculated at point in time.

+ References

+ Details

Name:	us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Weighted average remaining lease term for operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant