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Goodwill and Intangible Assets - Narrative (Details) - USD ($)		3 Months Ended		6 Months Ended
	Jul. 04, 2022	Apr. 02, 2023	Apr. 03, 2022	Apr. 02, 2023	Apr. 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		$ 12,100,000	$ 3,200,000	$ 15,500,000	$ 5,900,000
GSG
Goodwill [Line Items]
Gross amounts of goodwill		644,900,000		644,900,000		$ 536,800,000
Accumulated impairment		17,700,000		17,700,000		17,700,000
CIG
Goodwill [Line Items]
Gross amounts of goodwill		1,350,700,000		1,350,700,000		712,800,000
Accumulated impairment		$ 121,500,000		$ 121,500,000		$ 121,500,000