Long-term Debt and Line of Credit - Narrative (Details) - USD ($)		12 Months Ended
	Aug. 09, 2022	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Debt Instrument [Line Items]
Debt issuance cost, gross, noncurrent		$ 0	$ 9,100,000
Amortization of debt issuance costs		2,200,000	1,300,000	$ 700,000
A&R Term Loan
Debt Instrument [Line Items]
Maximum borrowing capacity	$ 445,000,000
A&R Revolving Facility
Debt Instrument [Line Items]
Letters of credit outstanding, amount		$ 700,000	400,000
A&R Credit Facility
Debt Instrument [Line Items]
Maximum borrowing capacity	65,000,000
Increase in revolving commitment	$ 125,000,000
Write off of deferred debt issuance cost			$ 400,000
A&R Credit Facility | Secured Overnight Financing Rate (SOFR) | Minimum
Debt Instrument [Line Items]
Debt instrument, variable interest rate	1.75%
A&R Credit Facility | Secured Overnight Financing Rate (SOFR) | Maximum
Debt Instrument [Line Items]
Debt instrument, variable interest rate	2.75%
A&R Credit Facility | Swingline Loans
Debt Instrument [Line Items]
Maximum borrowing capacity	$ 5,000,000
A&R Credit Facility | Letter of Credit
Debt Instrument [Line Items]
Maximum borrowing capacity	$ 5,000,000