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Benefit Plans - Narrative (Details) - USD ($)
 12 Months Ended
Oct. 02, 2021
Oct. 03, 2020
Sep. 28, 2019
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 $ 500,000 $ 2,200,000 $ 2,200,000
Medical, dental and accident and sickness benefit expense 13,800,000 14,900,000 12,100,000
Bonus liabilities 0    
Pension Plan      
Defined Benefit Plan Disclosure [Line Items]      
Employer contribution 4,920,000 500,000  
Benefits paid 7,253,000 8,213,000  
Benefit obligation 160,088,000 $ 169,741,000 $ 163,572,000
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