Related Party Transactions (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 29, 2024	Jun. 30, 2024	Mar. 31, 2024	Dec. 31, 2023	Oct. 01, 2023	Jul. 02, 2023	Apr. 02, 2023	Jan. 01, 2023	Sep. 29, 2024	Oct. 01, 2023	Oct. 02, 2022
Related Party Transaction [Line Items]
Revenue	$ 1,374,473	$ 1,344,323	$ 1,251,616	$ 1,228,267	$ 1,260,611	$ 1,208,947	$ 1,158,226	$ 894,766	$ 5,198,679	$ 4,522,550	$ 3,504,048
Reimbursable costs									61,637	78,489	91,656
Accounts receivable, net	1,051,461				974,535				1,051,461	974,535
Contract assets	129,678				113,939				129,678	113,939
Contract liabilities	(351,738)				(335,044)				(351,738)	(335,044)
Related Party
Related Party Transaction [Line Items]
Revenue									67,744	83,148	$ 95,967
Accounts receivable, net	15,612				19,944				15,612	19,944
Contract assets	1,625				2,723				1,625	2,723
Contract liabilities	$ (4,237)				$ (3,158)				$ (4,237)	$ (3,158)