Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 30, 2023	Sep. 30, 2023	Dec. 24, 2022
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	$ 737,800	$ 737,800	$ 737,800
Accumulated Amortization	(207,600)	(199,400)	(173,900)
Accumulated Impairment	(41,200)	(41,200)	(29,800)
Net Carrying Value	489,058	497,228	534,207
Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	274,600	274,600	274,600
Accumulated Amortization	(21,700)	(21,500)	(20,900)
Accumulated Impairment	(29,400)	(29,400)	(26,000)
Net Carrying Value	223,500	223,700	227,700
Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	46,800	46,800	46,800
Accumulated Amortization	(31,500)	(30,500)	(27,600)
Accumulated Impairment	(1,500)	(1,500)	(1,200)
Net Carrying Value	13,800	14,800	18,100
Amortizable | Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	22,100	22,100	22,100
Accumulated Amortization	(21,700)	(21,500)	(20,900)
Accumulated Impairment	0	0	0
Net Carrying Value	400	600	1,200
Amortizable | Customer-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	416,400	416,400	416,400
Accumulated Amortization	(154,400)	(147,400)	(125,400)
Accumulated Impairment	(10,300)	(10,300)	(2,500)
Net Carrying Value	251,800	258,800	288,400
Amortizable | Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	39,700	39,700	39,700
Accumulated Amortization	(31,500)	(30,500)	(27,600)
Accumulated Impairment	(300)	(300)	0
Net Carrying Value	7,900	8,900	12,200
Nonamortizable | Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	252,500	252,500	252,500
Accumulated Amortization	0	0	0
Accumulated Impairment	(29,400)	(29,400)	(26,000)
Net Carrying Value	223,100	223,100	226,500
Nonamortizable | Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	7,100	7,100	7,100
Accumulated Amortization	0	0	0
Accumulated Impairment	(1,200)	(1,200)	(1,200)
Net Carrying Value	$ 5,900	$ 5,900	$ 5,900