Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 28, 2024	Sep. 28, 2024	Dec. 30, 2023
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	$ 760,800	$ 760,800	$ 737,800
Accumulated Amortization	(240,900)	(233,500)	(207,600)
Accumulated Impairment	(54,000)	(54,000)	(41,200)
Net Carrying Value	465,914	473,280	489,058
Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	292,300	292,300	274,600
Accumulated Amortization	(23,000)	(22,800)	(21,700)
Accumulated Impairment	(35,000)	(35,000)	(29,400)
Net Carrying Value	234,400	234,500	223,500
Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	46,800	46,800	46,800
Accumulated Amortization	(35,100)	(34,300)	(31,500)
Accumulated Impairment	(1,500)	(1,500)	(1,500)
Net Carrying Value	10,200	11,000	13,800
Amortizable | Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	26,000	26,000	22,100
Accumulated Amortization	(23,000)	(22,800)	(21,700)
Accumulated Impairment	0	0	0
Net Carrying Value	3,000	3,100	400
Amortizable | Customer-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	421,700	421,700	416,400
Accumulated Amortization	(182,800)	(176,400)	(154,400)
Accumulated Impairment	(17,500)	(17,500)	(10,300)
Net Carrying Value	221,400	227,800	251,800
Amortizable | Other acquired intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	39,700	39,700	39,700
Accumulated Amortization	(35,100)	(34,300)	(31,500)
Accumulated Impairment	(300)	(300)	(300)
Net Carrying Value	4,300	5,100	7,900
Nonamortizable | Marketing-related intangible assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	266,300	266,300	252,500
Accumulated Amortization	0	0	0
Accumulated Impairment	(35,000)	(35,000)	(29,400)
Net Carrying Value	231,400	231,400	223,100
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