Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 29, 2024	Oct. 01, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 314,846	$ 270,453
Accumulated Amortization	(154,261)	(96,517)
Net Amount	$ 160,585	173,936
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	8 years 3 months 18 days
Gross Amount	$ 198,726	169,217
Accumulated Amortization	(57,975)	(36,072)
Net Amount	$ 140,751	133,145
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	4 months 24 days
Gross Amount	$ 75,194	63,825
Accumulated Amortization	(71,101)	(47,802)
Net Amount	$ 4,093	16,023
Trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	1 year 4 months 24 days
Gross Amount	$ 40,926	37,411
Accumulated Amortization	(25,185)	(12,643)
Net Amount	$ 15,741	$ 24,768