Benefit Plans - Narrative (Details) - USD ($)	12 Months Ended
	Sep. 30, 2023	Oct. 01, 2022	Oct. 02, 2021
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	$ 1,300,000	$ 1,600,000	$ 500,000
Medical, dental and accident and sickness benefit expense	15,300,000	13,600,000	13,800,000
Bonus liabilities	8,300,000	0
Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Employer contribution	1,113,000	0
Benefits paid	13,175,000	8,592,000
Benefit obligation	108,393,000	$ 122,571,000	$ 160,088,000
Estimated net loss to be amortized from accumulated other comprehensive loss over next fiscal year	700,000
Estimated future employer contributions in next fiscal year	0
Pension Plan, Certain Participants Meeting Certain Specified Criteria
Defined Benefit Plan Disclosure [Line Items]
Employer contribution	$ 5,200,000