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Revenue - Additional Information (Details) | Sep. 30, 2023 country
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Non-US And UK |
Disaggregation of Revenue [Line Items] |
Number of countries in which entity operates | 32

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- 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_DisaggregationOfRevenueLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition The number of countries in which the entity operates as of balance sheet date. + References No definition available. + Details
Name: | us-gaap_NumberOfCountriesInWhichEntityOperates
Namespace Prefix: | us-gaap_
Data Type: | xbrli:integerItemType
Balance Type: | na
Period Type: | instant

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- Details
Name: | srt_StatementGeographicalAxis=stgw_NonUSAndUKMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |