Leases - Additional Information (Details) $ in Millions	Sep. 30, 2025 USD ($) lease
Leases [Abstract]
Number of leases not yet commenced \| lease	1
Leases not yet commenced, liability \| $	$ 11.3

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

No definition available.

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