Discontinued Operations - Schedule of Notable Components Included In Consolidated Statements of Cash Flows For These Discontinued Operations (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 27, 2024	Sep. 29, 2023	Sep. 30, 2022
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Intangible assets	$ 209,507	$ 203,906	$ 198,602
Discontinued Operations, Spinoff | SpinCo Business
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Property, equipment and improvements	16,245	19,075
Intangible assets	56,839	56,675
Deferred income taxes	(106,424)	(5,297)
Additions to property and equipment	$ (13,067)	$ (26,448)