Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Mar. 25, 2023	Sep. 24, 2022	Mar. 26, 2022
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	$ 737,800	$ 737,800	$ 673,500
Accumulated Amortization	(182,800)	(164,900)	(144,500)
Accumulated Impairment	(29,800)	(29,800)	(29,800)
Net Carrying Value	525,301	543,210	499,251
Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	274,600	274,600	240,300
Accumulated Amortization	(21,100)	(20,500)	(19,800)
Accumulated Impairment	(26,000)	(26,000)	(26,000)
Net Carrying Value	227,500	228,000	194,400
Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	46,800	46,800	46,800
Accumulated Amortization	(28,600)	(26,600)	(24,500)
Accumulated Impairment	(1,200)	(1,200)	(1,200)
Net Carrying Value	17,100	19,100	21,100
Amortizable | Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	22,100	22,100	22,100
Accumulated Amortization	(21,100)	(20,500)	(19,800)
Accumulated Impairment	0	0	0
Net Carrying Value	1,000	1,500	2,200
Amortizable | Customer-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	416,400	416,400	386,400
Accumulated Amortization	(133,100)	(117,800)	(100,200)
Accumulated Impairment	(2,500)	(2,500)	(2,500)
Net Carrying Value	280,800	296,100	283,700
Amortizable | Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	39,700	39,700	39,700
Accumulated Amortization	(28,600)	(26,600)	(24,500)
Accumulated Impairment	0	0	0
Net Carrying Value	11,100	13,200	15,200
Nonamortizable | Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	252,500	252,500	218,200
Accumulated Amortization	0	0	0
Accumulated Impairment	(26,000)	(26,000)	(26,000)
Net Carrying Value	226,500	226,500	192,200
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