Summary of Significant Accounting Policies and Recently Issued Accounting Standards - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 01, 2022	Oct. 02, 2021	Oct. 03, 2020	Sep. 13, 2018
Finite-Lived Intangible Assets [Line Items]
Deferred financing fees	$ 1.4	$ 2.0		$ 2.0
Debt amortization/ Non-cash interest expense	$ 1.5	1.1	$ 0.9
Product Warranty Liability [Line Items]
Extended product warranty, period	12 months
Research and development expense	$ 6.1	$ 5.2	$ 6.4
Minimum
Product Warranty Liability [Line Items]
Standard product warranty, period	1 year
Extended product warranty, period	2 years
Maximum
Product Warranty Liability [Line Items]
Standard product warranty, period	5 years
Extended product warranty, period	5 years
Engineering designs | Maximum
Finite-Lived Intangible Assets [Line Items]
Estimated life	7 years
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Estimated life	20 years