Mergers and Acquisitions - Narrative (Details) $ / shares in Units, $ in Thousands	12 Months Ended
	Sep. 28, 2024 USD ($) event $ / shares shares	Sep. 24, 2022 USD ($)	Sep. 30, 2023 shares	Jun. 07, 2022 shares
Business Acquisition [Line Items]
Number of triggering events achieved | event	3
Conversion of stock (in shares)	9,040,000
Cash proceeds from forward purchase agreement | $		$ 200,000
Repurchase of shares | $	$ 300,000	300,000
Net contributions from the Business Combination | $	84,700	84,672
Transaction costs | $	$ 37,100	$ 37,104
Trigger Event One
Business Acquisition [Line Items]
Contingent consideration payable, earnout (in dollars per share) | $ / shares	$ 12.00
Trigger Event Two
Business Acquisition [Line Items]
Contingent consideration payable, earnout (in dollars per share) | $ / shares	14.00
Trigger Event Three
Business Acquisition [Line Items]
Contingent consideration payable, earnout (in dollars per share) | $ / shares	$ 16.00
Tranche One | Sponsor Shares
Business Acquisition [Line Items]
Award vesting rights, percentage	60.00%
Redeemed (in shares)	5,424,000
Tranche Two | Sponsor Shares
Business Acquisition [Line Items]
Award vesting rights, percentage	20.00%
Redeemed (in shares)	1,808,000
Tranche Three | Sponsor Shares
Business Acquisition [Line Items]
Award vesting rights, percentage	20.00%
Redeemed (in shares)	1,808,000
PIPE
Business Acquisition [Line Items]
Sale of stock, consideration received on transaction | $	$ 205,000
Sale of stock (in dollars per share) | $ / shares	$ 10.00
Forward Purchase Investor
Business Acquisition [Line Items]
Sale of stock (in dollars per share) | $ / shares	$ 10.00
Cash proceeds from forward purchase agreement | $	$ 200,000
Class A Common Stock
Business Acquisition [Line Items]
Common stock, par value (in dollars per share) | $ / shares	$ 0.0001
Common stock, issued (in shares)	104,689,377		82,112,881
Contingent consideration payable, earnout (in shares)	20,000,000.0
Class A Common Stock | Trigger Event One
Business Acquisition [Line Items]
Contingent consideration payable, earnout (in shares)	6,666,667
Class A Common Stock | Trigger Event Two
Business Acquisition [Line Items]
Contingent consideration payable, earnout (in shares)	6,666,667
Class A Common Stock | Trigger Event Three
Business Acquisition [Line Items]
Contingent consideration payable, earnout (in shares)	6,666,666
Class A Common Stock | PIPE
Business Acquisition [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	20,500,000
Class A Common Stock | Forward Purchase Investor
Business Acquisition [Line Items]
Sale of stock, number of shares issued in transaction (in shares)	20,000,000.0
Common Class B
Business Acquisition [Line Items]
Common stock, par value (in dollars per share) | $ / shares	$ 0.0001
Class V-1 Common Stock
Business Acquisition [Line Items]
Common stock, par value (in dollars per share) | $ / shares	$ 0.0001
Common stock, issued (in shares)	76,965,386		66,931,097
Contingent consideration payable, earnout (in shares)	20,000,000.0
Class V-1 Common Stock | Warehouse
Business Acquisition [Line Items]
Common stock, issued (in shares)				60,844,573
Class V-3 Common Stock
Business Acquisition [Line Items]
Common stock, par value (in dollars per share) | $ / shares	$ 0.0001
Common stock, issued (in shares)	404,309,196		407,528,941
Class V-3 Common Stock | Warehouse
Business Acquisition [Line Items]
Common stock, issued (in shares)				416,933,025