Equity Investment in Affiliate - Summarized Financial Results (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2023	Oct. 01, 2022	Oct. 02, 2021
Schedule of Equity Method Investments [Line Items]
Assets, Current	$ 236,063	$ 174,476
Assets	417,766	366,126
Liabilities, Current	229,620	164,774
Liabilities, Noncurrent	148,148	199,970
Net sales	1,132,793	800,637	$ 683,995
Segment gross profit	138,850	36,546	72,141
Operating profit	51,657	(40,700)	6,522
Net income (loss)	23,812	(45,759)	(289)
Micro Bird Holdings, Inc.
Schedule of Equity Method Investments [Line Items]
Assets, Current	72,232	46,951
Assets, Noncurrent	21,220	20,625
Assets	93,452	67,576
Liabilities, Current	64,230	53,022
Liabilities, Noncurrent	2,359	1,036
Liabilities	66,589	54,058
Net Assets	26,863	13,518
Net sales	203,086	128,343	131,028
Segment gross profit	35,453	2,071	10,370
Operating profit	18,310	(10,453)	1,602
Net income (loss)	$ 13,244	$ (8,924)	$ 1,438