Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	6 Months Ended
	Mar. 31, 2024	Oct. 01, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 298,734	$ 270,453
Accumulated Amortization	(123,123)	(96,517)
Net Amount	$ 175,611	173,936
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	8 years 8 months 12 days
Gross Amount	$ 188,940	169,217
Accumulated Amortization	(45,970)	(36,072)
Net Amount	$ 142,970	133,145
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	8 months 12 days
Gross Amount	$ 71,161	63,825
Accumulated Amortization	(58,761)	(47,802)
Net Amount	$ 12,400	16,023
Trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	1 year 10 months 24 days
Gross Amount	$ 38,633	37,411
Accumulated Amortization	(18,392)	(12,643)
Net Amount	$ 20,241	$ 24,768