Income Taxes - Schedule of Temporary Differences Comprising the Net Deferred Income Tax Liability (Details) - USD ($) $ in Thousands	Oct. 01, 2023	Oct. 02, 2022
Deferred Tax Assets:
State taxes	$ 2,686	$ 1,238
Reserves and contingent liabilities	2,849	5,023
Accounts receivable including the allowance for doubtful accounts	5,323	4,986
Accrued liabilities	64,155	35,973
Lease liabilities, operating leases	53,437	49,618
Stock-based compensation	1,900	2,925
Unbilled revenue	3,090	4,885
Loss and other carry-forwards	62,777	41,648
Property and equipment	552	0
Capitalized research and development	17,778	0
Capped call transactions	12,696	0
Valuation allowance	(11,663)	(12,286)
Total deferred tax assets	215,580	134,010
Deferred Tax Liabilities:
Prepaid expense	(2,703)	(6,065)
Right-of-use assets, operating leases	(53,437)	(49,618)
Intangibles	(83,242)	(42,863)
Undistributed earnings	(1,453)	(2,200)
Property and equipment	0	(621)
Total deferred tax liabilities	(140,835)	(101,367)
Net deferred tax assets	$ 74,745	$ 32,643