Pension and Other Postretirement Benefit Plans - Schedule of Components of Net Periodic Pension Cost (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 29, 2023	Sep. 30, 2022	Oct. 01, 2021
Defined Benefit Plan Disclosure [Line Items]
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) Excluding Service Cost, Statement of Income or Comprehensive Income [Extensible Enumeration]	Nonoperating Income (Expense)	Nonoperating Income (Expense)	Nonoperating Income (Expense)
Pension Plan | U.S. Plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	$ 140	$ 236	$ 456
Interest cost	15,629	10,350	10,221
Expected return on plan assets	(19,496)	(16,933)	(15,932)
Actuarial (gains) losses	(1,770)	2,861	4,249
Prior service cost	430	430	431
Net pension cost (income), before special items	(5,067)	(3,056)	(575)
Curtailment expense/Settlement (gains) losses	0	(206)	(64)
Total net periodic pension cost (income) recognized	(5,067)	(3,262)	(639)
Pension Plan | Non-U.S. Plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	6,926	6,480	6,568
Interest cost	74,077	42,328	38,907
Expected return on plan assets	(73,387)	(71,875)	(90,346)
Actuarial (gains) losses	6,317	7,147	10,834
Prior service cost	1,424	1,421	1,519
Net pension cost (income), before special items	15,357	(14,499)	(32,518)
Curtailment expense/Settlement (gains) losses	208	329	2,847
Total net periodic pension cost (income) recognized	$ 15,565	$ (14,170)	$ (29,671)