Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	9 Months Ended
	Jul. 02, 2023	Oct. 02, 2022
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 312,628	$ 87,673
Accumulated Amortization	(87,596)	(58,510)
Net Amount	$ 225,032	29,163
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	7 years 2 months 12 days
Gross Amount	$ 226,024	41,676
Accumulated Amortization	(36,952)	(21,092)
Net Amount	$ 189,072	20,584
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	10 months 24 days
Gross Amount	$ 57,342	33,286
Accumulated Amortization	(41,616)	(29,990)
Net Amount	$ 15,726	3,296
Trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	2 years 8 months 12 days
Gross Amount	$ 29,262	12,711
Accumulated Amortization	(9,028)	(7,428)
Net Amount	$ 20,234	$ 5,283