Goodwill and Intangible Assets - Narrative (Details) - USD ($)		3 Months Ended		6 Months Ended
	Jul. 03, 2023	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023	Oct. 01, 2023
Goodwill [Line Items]
Impairment of goodwill	$ 0
Percentage of excess of fair value over carrying value (less than)	45.00%
Amortization expense		$ 12,100,000	$ 12,100,000	$ 24,600,000	$ 15,500,000
GSG
Goodwill [Line Items]
Gross amounts of goodwill		750,900,000		750,900,000		$ 677,600,000
Accumulated impairment		17,700,000		17,700,000		17,700,000
CIG
Goodwill [Line Items]
Gross amounts of goodwill		1,366,000,000		1,366,000,000		1,341,800,000
Accumulated impairment		$ 121,500,000		$ 121,500,000		$ 121,500,000