Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Mar. 28, 2026	Sep. 27, 2025	Mar. 29, 2025
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	$ 763,000	$ 763,000	$ 763,000
Accumulated Amortization	(273,000)	(260,400)	(247,400)
Accumulated Impairment	(55,000)	(55,000)	(54,000)
Net Carrying Value	434,953	447,643	461,657
Marketing-Related Intangible Assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	292,300	292,300	292,300
Accumulated Amortization	(23,400)	(23,300)	(23,100)
Accumulated Impairment	(35,000)	(35,000)	(35,000)
Net Carrying Value	233,900	234,100	234,300
Other Acquired Intangible Assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	49,100	49,100	49,100
Accumulated Amortization	(36,200)	(35,800)	(35,400)
Accumulated Impairment	(2,500)	(2,500)	(1,500)
Net Carrying Value	10,300	10,700	12,200
Amortizable | Marketing-Related Intangible Assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	26,000	26,000	26,000
Accumulated Amortization	(23,400)	(23,300)	(23,100)
Accumulated Impairment	0	0	0
Net Carrying Value	2,500	2,700	2,900
Amortizable | Customer-Related Intangible Assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	421,700	421,700	421,700
Accumulated Amortization	(213,400)	(201,300)	(188,900)
Accumulated Impairment	(17,500)	(17,500)	(17,500)
Net Carrying Value	190,800	202,900	215,200
Amortizable | Other Acquired Intangible Assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	41,900	41,900	41,900
Accumulated Amortization	(36,200)	(35,800)	(35,400)
Accumulated Impairment	(1,300)	(1,300)	(300)
Net Carrying Value	4,400	4,800	6,300
Nonamortizable | Marketing-Related Intangible Assets
Acquired Indefinite-lived Intangible Assets [Line Items]
Gross	266,300	266,300	266,300
Accumulated Amortization	0	0	0
Accumulated Impairment	(35,000)	(35,000)	(35,000)
Net Carrying Value	231,400	231,400	231,400
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