Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	6 Months Ended
	Mar. 30, 2025	Sep. 29, 2024
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 305,495	$ 314,846
Accumulated Amortization	(168,711)	(154,261)
Net Amount	$ 136,784	160,585
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	7 years 10 months 24 days
Gross Amount	$ 193,216	198,726
Accumulated Amortization	(66,387)	(57,975)
Net Amount	$ 126,829	140,751
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	1 month 6 days
Gross Amount	$ 72,881	75,194
Accumulated Amortization	(72,639)	(71,101)
Net Amount	$ 242	4,093
Trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	10 months 24 days
Gross Amount	$ 39,398	40,926
Accumulated Amortization	(29,685)	(25,185)
Net Amount	$ 9,713	$ 15,741