Revenue and Contract Balances - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 01, 2023	Oct. 02, 2022
Disaggregation of Revenue [Line Items]
Contract liability revenue recognized during the period	$ 164,000	$ 125,000
Net favorable operating income adjustments	11,000
Liabilities for anticipated losses	8,500	10,000
Estimated cost to complete the related contracts	$ 68,000	$ 80,000
Period for billing and collecting unbilled receivables	12 months
Remaining unsatisfied performance obligation	$ 4,755,077
Remaining performance obligation, termination notice period one	30 days
Remaining performance obligation, termination notice period two	60 years
Remaining performance obligation, termination notice period three	90 days