Income Taxes - Schedule of Domestic and Foreign Components of Income (Loss) Before Income Taxes (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023	Oct. 01, 2022
Income Tax Disclosure [Abstract]
U.S.	$ (114,757)	$ (84,557)	$ (64,267)
Foreign	244,289	245,570	222,570
Income before income taxes	$ 129,532	$ 161,013	$ 158,303