Goodwill and Intangible Assets - Narrative (Details) - USD ($)		3 Months Ended		9 Months Ended
	Jul. 04, 2022	Jul. 02, 2023	Jul. 03, 2022	Jul. 02, 2023	Jul. 03, 2022	Oct. 02, 2022
Goodwill [Line Items]
Impairment of goodwill	$ 0
Percentage of excess of fair value over carrying value (less than)	165.00%
Amortization expense		$ 14,100,000	$ 3,700,000	$ 29,600,000	$ 9,600,000
GSG
Goodwill [Line Items]
Gross amounts of goodwill		646,400,000		646,400,000		$ 536,800,000
Accumulated impairment		17,700,000		17,700,000		17,700,000
CIG
Goodwill [Line Items]
Gross amounts of goodwill		1,379,700,000		1,379,700,000		712,800,000
Accumulated impairment		$ 121,500,000		$ 121,500,000		$ 121,500,000