Goodwill and Intangible Assets - Narrative (Details) - USD ($)		3 Months Ended		9 Months Ended
	Jul. 03, 2023	Jun. 30, 2024	Jul. 02, 2023	Jun. 30, 2024	Jul. 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		$ 13,800,000	$ 14,100,000	$ 38,400,000	$ 29,600,000
GSG
Goodwill [Line Items]
Gross amounts of goodwill		764,800,000		764,800,000		$ 677,600,000
Accumulated impairment		17,700,000		17,700,000		17,700,000
CIG
Goodwill [Line Items]
Gross amounts of goodwill		1,366,500,000		1,366,500,000		1,341,800,000
Accumulated impairment		$ 121,500,000		$ 121,500,000		$ 121,500,000