Components of Accrued Expenses and Other Current Liabilities (Detail) - USD ($) $ in Thousands	Sep. 30, 2025	Sep. 30, 2024
Payables and Accruals [Abstract]
Accrued wages and benefits	$ 30,724	$ 27,710
Self-insurance liabilities	78,772	76,718
Other accrued expenses and other current liabilities	10,001	11,889
Total accrued expenses and other current liabilities	$ 119,497	$ 116,317

Accrued Wages And Benefits

No definition available.

Name:	sgu_AccruedWagesAndBenefits
Namespace Prefix:	sgu_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of obligations incurred through that date and payable to insurance entities to mitigate potential loss from various risks or to satisfy a promise to provide certain coverage's to employees. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable, pertaining to costs that are statutory in nature, are incurred on contractual obligations, or accumulate over time and for which invoices have not yet been received or will not be rendered. Examples include taxes, interest, rent and utilities. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

+ Details

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

- Definition

Amount of expenses incurred but not yet paid classified as other, due within one year or the normal operating cycle, if longer.

+ References

+ Details

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

- References

No definition available.

+ Details

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