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Leases - Additional Information (Details) $ in Millions	9 Months Ended
	Sep. 30, 2023 USD ($) lease
Leases [Abstract]
Number of leases not yet commenced | lease	3
Leases not yet commenced, liability	$ 6.0
ROU Lease and LHI, Impairment Loss	$ 9.2

X

- Definition

Lessee, Operating Lease, Lease Not yet Commenced, Number of Contracts

+ References

No definition available.

+ Details

Name:	stgw_LesseeOperatingLeaseLeaseNotYetCommencedNumberOfContracts
Namespace Prefix:	stgw_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Lessee, Operating Lease, Lease Not yet Commenced, Liability

+ References

No definition available.

+ Details

Name:	stgw_LesseeOperatingLeaseLeaseNotyetCommencedLiability
Namespace Prefix:	stgw_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

ROU Lease and LHI, Impairment Loss

+ References

No definition available.

+ Details

Name:	stgw_ROULeaseAndLHIImpairmentLoss
Namespace Prefix:	stgw_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- References

No definition available.

+ Details

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