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Unit-Based Compensation Arrangements - Additional Information (Details) - USD ($)
$ in Thousands
 3 Months Ended
Dec. 28, 2024
Dec. 30, 2023
Sep. 28, 2024
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Restricted unit awards vesting percentage 33.33%    
Distribution Equivalent Rights Plan [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Compensation expense $ 354 $ 375  
Distribution Equivalent Rights Plan, terms On January 17, 2017, the Partnership adopted the Distribution Equivalent Rights Plan (the “DER Plan”), as amended on November 8, 2022, which gives the Compensation Committee discretion to award distribution equivalent rights (“DERs”) to executive officers of the Partnership. Once awarded, DERs entitle the grantee to a cash payment each time the Board of Supervisors declares a cash distribution on the Partnership’s Common Units, which cash payment will be equal to an amount calculated by multiplying the number of unvested restricted units and unvested phantom units which are held by the grantee on the record date of the distribution, by the amount of the declared distribution per Common Unit    
Phantom Equity Plan [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Compensation expense $ 1,574 2,019  
Liability included within accrued employment and benefit costs (or other liabilities, as applicable) related to estimated future payments under the LTIP 6,458   $ 9,019
Restricted Stock Units (RSUs) [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Unrecognized compensation cost $ 7,508    
Weighted-average recognition period of compensation cost 1 year    
Compensation expense $ 2,379 2,645  
Restricted Stock Units (RSUs) [Member] | Maximum [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Total number of Common Units authorized for issuance (in units) 1,800,000    
2018 Restricted Unit Plan [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Restricted Unit Plans, terms of award Unless otherwise determined by the Compensation Committee of the Partnership’s Board of Supervisors (the “Compensation Committee”) on or before the grant date, one-third of all outstanding awards under the Restricted Unit Plan will vest on each of the first three anniversaries of the award grant date. Participants in the Restricted Unit Plan are not eligible to receive quarterly distributions on, or vote, their respective restricted units until vested. Restricted units cannot be sold or transferred prior to vesting. The value of each restricted unit is established by the market price of the Common Unit on the date of grant, net of estimated future distributions during the vesting period    
Awards Granted 477,667    
Aggregate grant date fair value of restricted units awarded $ 7,119    
2018 Restricted Unit Plan [Member] | Maximum [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Total number of Common Units authorized for issuance (in units) 6,175,000    
2018 Restricted Unit Plan [Member] | May 18, 2021[Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Additional number of Common Units authorized for issuance (in units) 1,725,000    
2018 Restricted Unit Plan [Member] | May 21, 2024 [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Additional number of Common Units authorized for issuance (in units) 2,650,000    
Long-Term Incentive Plan [Member]      
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]      
Long-Term Incentive Plan, terms of award The LTIP is a non-qualified, unfunded, long-term incentive plan for executive officers and key employees that provides for payment, in the form of cash, of an award of equity-based compensation at the end of a three-year performance period.    
Measurement period of average distribution coverage ratio 3 years    
Long-Term Incentive Plan, compensation earned, description The level of compensation earned under the fiscal 2022 award and awards thereafter is evaluated using two separate measurement components: (i) 50% weight based on the level of average distributable cash flow of the Partnership over the three-year measurement period; and (ii) 50% weight based on the achievement of certain operating and strategic objectives, set by the Compensation Committee for that    
Compensation expense (income) $ 3,585 2,462  
Liability included within accrued employment and benefit costs (or other liabilities, as applicable) related to estimated future payments under the LTIP 10,666   $ 11,120
Cash payouts $ 4,038 $ 4,405