Commitments, Contingencies and Guarantees (Details Textual) $ in Millions	Dec. 31, 2023 USD ($)
Commitments and Contingencies Disclosure [Abstract]
2023	$ 7.3
2024	7.0
2025	4.2
2026	3.0
2027	3.1
Thereafter	3.8
Cloud Purchase Obligation, to be Paid, Year One	5.7
Cloud Purchase Obligation, to be Paid, Year Two	6.9
Cloud Purchase Obligation, to be Paid, Year Three	8.7
Cloud Purchase Obligation, to be Paid, Year Four	10.4
Cloud Purchase Obligation, to be Paid, Year Five	12.7
Cloud Purchase Obligation, to be paid, after Year Five	$ 15.3

Cloud Purchase Obligation, to be paid, after Year Five

No definition available.

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Namespace Prefix:	stgw_
Data Type:	xbrli:monetaryItemType
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Period Type:	instant

- Definition

Cloud Purchase Obligation, to be Paid, Year Five

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No definition available.

+ Details

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

- Definition

Cloud Purchase Obligation, to be Paid, Year Four

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No definition available.

+ Details

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

- Definition

Cloud Purchase Obligation, to be Paid, Year One

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No definition available.

+ Details

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

- Definition

Cloud Purchase Obligation, to be Paid, Year Three

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No definition available.

+ Details

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

- Definition

Cloud Purchase Obligation, to be Paid, Year Two

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No definition available.

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

- References

No definition available.

+ Details

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- Definition

Amount of purchase arrangement to be paid after fifth fiscal year following current fiscal year. Includes, but is not limited to, recorded and unrecorded purchase obligations, long-term purchase commitment, and short-term purchase commitment. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

No definition available.

+ Details

Name:	us-gaap_PurchaseObligationDueAfterFifthYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of purchase arrangement to be paid in fifth fiscal year following current fiscal year. Includes, but is not limited to, recorded and unrecorded purchase obligations, long-term purchase commitment, and short-term purchase commitment. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of purchase arrangement to be paid in fourth fiscal year following current fiscal year. Includes, but is not limited to, recorded and unrecorded purchase obligations, long-term purchase commitment, and short-term purchase commitment. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of purchase arrangement to be paid in next fiscal year following current fiscal year. Includes, but is not limited to, recorded and unrecorded purchase obligations, long-term purchase commitment, and short-term purchase commitment. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of purchase arrangement to be paid in second fiscal year following current fiscal year. Includes, but is not limited to, recorded and unrecorded purchase obligations, long-term purchase commitment, and short-term purchase commitment. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of purchase arrangement to be paid in third fiscal year following current fiscal year. Includes, but is not limited to, recorded and unrecorded purchase obligations, long-term purchase commitment, and short-term purchase commitment. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant