Acquisitions - Changes in the Carrying Value of Estimated Contingent Earn-Out Liabilities (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 01, 2023	Oct. 02, 2022	Oct. 03, 2021
Earn-out payments:
Reported as cash used in financing activities	$ (21,328)	$ (20,124)	$ (20,251)
Contingent consideration
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning balance	65,566	59,297	32,617
Acquisition date fair value of contingent earn-out liabilities	12,248	31,341	50,235
Foreign exchange impact	2,201	(7,152)	(596)
Earn-out payments:
Reported as cash used in operating activities	0	(310)	(427)
Reported as cash used in financing activities	(21,328)	(20,123)	(20,251)
Ending balance	$ 73,422	$ 65,566	$ 59,297
Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Liability, Gain (Loss), Statement of Other Comprehensive Income or Comprehensive Income [Extensible Enumeration]	(Loss) gain on cash flow hedge valuations, net of tax	(Loss) gain on cash flow hedge valuations, net of tax	(Loss) gain on cash flow hedge valuations, net of tax
Interest expense | Contingent consideration
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Earnings adjustment to contingent earn-out liabilities	$ 2,480	$ 2,184	$ 992
Operating income | Contingent consideration
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Earnings adjustment to contingent earn-out liabilities	$ 12,255	$ 329	$ (3,273)