Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	9 Months Ended
	Jun. 30, 2024	Oct. 01, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 301,681	$ 270,453
Accumulated Amortization	(137,222)	(96,517)
Net Amount	$ 164,459	173,936
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	8 years 4 months 24 days
Gross Amount	$ 190,329	169,217
Accumulated Amortization	(50,980)	(36,072)
Net Amount	$ 139,349	133,145
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	7 months 6 days
Gross Amount	$ 72,579	63,825
Accumulated Amortization	(65,050)	(47,802)
Net Amount	$ 7,529	16,023
Trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	1 year 8 months 12 days
Gross Amount	$ 38,773	37,411
Accumulated Amortization	(21,192)	(12,643)
Net Amount	$ 17,581	$ 24,768