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Income Taxes - Schedule of Effective Income Tax Rate Reconciliation (Details) - USD ($)
$ in Thousands
12 Months Ended
Oct. 01, 2022
Oct. 02, 2021
Oct. 03, 2020
Income Tax Disclosure [Abstract]      
U.S. federal income taxes at statutory rate $ 14,433 $ 32,954 $ (4,217)
U.S. state and local income taxes, net of federal benefit and state credits (2,594) (9,473) (2,798)
Foreign income tax rate differential 970 1,430 (75)
Stock-based compensation (15,532) (47,496) 869
Federal research and development tax credits (8,983) (21,535) (8,012)
Unrecognized federal tax benefits (2,482) 4,041 815
Change in tax rate 5,013 (2,681)  
Global intangible low taxed income, net of foreign tax credits 290    
162(m) executive compensation limitation 2,574    
Base erosion and anti-abuse tax     (781)
Other 1,079 (565) 598
Change in valuation allowance 6,579 41,655 13,633
Provision for income taxes $ 1,347 $ (1,670) $ 32