Goodwill and Intangible Assets - Narrative (Details) - USD ($)		12 Months Ended
	Jul. 03, 2023	Oct. 01, 2023	Oct. 02, 2022	Oct. 03, 2021
Goodwill [Line Items]
Impairment of goodwill	$ 0
Percentage of excess of fair value over carrying value (less than)	45.00%
Amortization expense for intangible assets		$ 41,200,000	$ 13,200,000	$ 11,500,000
Reduction in intangible assets, foreign currency translation adjustment		200,000	5,300,000
GSG
Goodwill [Line Items]
Gross amounts of goodwill		677,600,000	536,800,000
Accumulated impairment		17,700,000	17,700,000
CIG
Goodwill [Line Items]
Gross amounts of goodwill		1,341,800,000	712,800,000
Accumulated impairment		$ 121,500,000	$ 121,500,000