Equity Investment in Affiliate - Narrative (Details) $ in Thousands	12 Months Ended
	Sep. 30, 2023 USD ($)	Oct. 01, 2022 USD ($)	Oct. 02, 2021 USD ($)	Oct. 14, 2009 manufacturer
Schedule of Equity Method Investments [Line Items]
Number of manufacturers before venture | manufacturer				2
Equity investment in affiliate	$ 17,619	$ 10,659
Equity in net income (loss) of non-consolidated affiliate	$ 6,960	(4,159)	$ 498
Micro Bird Holdings, Inc.
Schedule of Equity Method Investments [Line Items]
Equity interest in equity method investment (as a percent)	50.00%
Equity investment in affiliate	$ 17,600	10,700
Equity in net income (loss) of non-consolidated affiliate	$ 7,000	$ (4,200)	$ 500