Benefit Plans - Amounts Recognized in Other Comprehensive Income (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2023	Oct. 01, 2022	Oct. 02, 2021
Defined Benefit Plan Disclosure [Line Items]
Net gain	$ (23,812)	$ 45,759	$ 289
Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Interest cost	6,035	4,368	4,227
Expected return on plan assets	(6,518)	(8,491)	(7,777)
Amortization of net loss	1,195	1,163	1,861
Net periodic benefit expense (income)	712	(2,960)	(1,689)
Net gain	(12,024)	(2,605)	(16,038)
Amortization of net loss	(1,195)	(1,163)	(1,861)
Total recognized in other comprehensive income	(13,219)	(3,768)	(17,899)
Total recognized in net periodic pension benefit expense (income) and other comprehensive income	$ (12,507)	$ (6,728)	$ (19,588)