Restructuring and Non-recurring Charges - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023	Oct. 01, 2022
Restructuring Cost and Reserve [Line Items]
Restructuring and other charges, net	$ 20,257	$ 23,094	$ 2,021
Amounts utilized	(18,274)	(22,584)	(1,980)
Restructuring Charges
Restructuring Cost and Reserve [Line Items]
Other Tax Expense (Benefit)	(2,100)	(1,900)	(200)
Termination and Severance Costs
Restructuring Cost and Reserve [Line Items]
Restructuring and other charges, net	14,130	8,865	1,766
Amounts utilized	(13,256)	(8,355)	(1,725)
Arbitration Charge
Restructuring Cost and Reserve [Line Items]
Restructuring and other charges, net	(2,250)	14,229	0
Amounts utilized	$ 2,250	$ (14,229)	$ 0