Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 01, 2023	Oct. 02, 2022
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 270,453	$ 87,673
Accumulated Amortization	(96,517)	(58,510)
Net Amount	$ 173,936	29,163
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	9 years 4 months 24 days
Gross Amount	$ 169,217	41,676
Accumulated Amortization	(36,072)	(21,092)
Net Amount	$ 133,145	20,584
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	10 months 24 days
Gross Amount	$ 63,825	33,286
Accumulated Amortization	(47,802)	(29,990)
Net Amount	$ 16,023	3,296
Trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	2 years 4 months 24 days
Gross Amount	$ 37,411	12,711
Accumulated Amortization	(12,643)	(7,428)
Net Amount	$ 24,768	$ 5,283