Benefit Plans - Narrative (Details) - USD ($)	12 Months Ended
	Oct. 01, 2022	Oct. 02, 2021	Oct. 03, 2020
Defined Benefit Plan Disclosure [Line Items]
Employer matching contribution, percent of employees' contribution	50.00%
Employer matching contribution, percent of employees' gross pay	6.00%
Employer discretionary contribution amount	$ 1,600,000	$ 500,000	$ 2,200,000
Medical, dental and accident and sickness benefit expense	13,600,000	13,800,000	14,900,000
Bonus liabilities	0
Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Employer contribution	0	4,920,000
Benefits paid	8,592,000	7,253,000
Benefit obligation	122,571,000	$ 160,088,000	$ 169,741,000
Estimated net loss to be amortized from accumulated other comprehensive loss over next fiscal year	1,200,000
Estimated future employer contributions in next fiscal year	$ 0