Debt - Additional Information (Details)		12 Months Ended
	Nov. 01, 2024 USD ($)	Sep. 30, 2025 USD ($)	Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Jun. 30, 2022 USD ($)
Debt Instrument [Line Items]
Long-term debt		$ 1,626,125,000
Fixed coverage ratio		5.76	11.32
Leverage ratio		3.10	1.81
Notional amount		$ 300,000,000.0	$ 300,000,000.0
Fair value of interest rate swaps		7,900,000	11,600,000
Interest expense, borrowings		95,100,000	23,200,000	$ 18,700,000
Amortization of deferred debt issuance costs		3,800,000	400,000	$ 300,000
Term Loan A
Debt Instrument [Line Items]
Long-term debt		592,500,000	392,200,000
Term Loan B
Debt Instrument [Line Items]
Long-term debt		$ 843,600,000	0.0
Term Loan | Term Loan A | Term Loan A
Debt Instrument [Line Items]
Maximum borrowing capacity					$ 600,000,000
Term Loan | Term Loan - 11 Quarters | Term Loan A
Debt Instrument [Line Items]
Line of credit, principal repayment rate		1.25%
Term Loan | Term Loan A/Revolver Credit Agreement | Term Loan A | Minimum
Debt Instrument [Line Items]
Fixed coverage ratio		3.00
Term Loan | Term Loan A/Revolver Credit Agreement | Term Loan A | Maximum | Debt Covenant Term, Period 1
Debt Instrument [Line Items]
Leverage ratio		4.50
Term Loan | Term Loan A/Revolver Credit Agreement | Term Loan A | Maximum | Debt Covenant Term, Period 2
Debt Instrument [Line Items]
Leverage ratio		4.25
Term Loan | Term Loan A/Revolver Credit Agreement | Term Loan A | Maximum | Debt Covenant Term, Period 3
Debt Instrument [Line Items]
Leverage ratio		4.00
Term Loan | Term Loan A/Revolver Credit Agreement | Term Loan A | Maximum | Debt Covenant Term, Period 4
Debt Instrument [Line Items]
Leverage ratio		3.75
Term Loan | Term Loan B Credit Agreement | Term Loan A
Debt Instrument [Line Items]
Maximum borrowing capacity	$ 850,000,000
Line of credit, principal repayment rate	0.25%
Proceeds from lines of credit	$ 850,000,000
Term Loan | Term Loan B Credit Agreement | Term Loan A | Federal Funds
Debt Instrument [Line Items]
Basis spread on variable rate	0.50%
Term Loan | Term Loan B Credit Agreement | Term Loan A | Term SOFR | Variable Rate Component One
Debt Instrument [Line Items]
Basis spread on variable rate	1.00%
Term Loan | Term Loan B Credit Agreement | Term Loan A | Term SOFR | Variable Rate Component Two
Debt Instrument [Line Items]
Basis spread on variable rate	2.50%
Term Loan | Term Loan B Credit Agreement | Term Loan A | Base Rate | Variable Rate Component One
Debt Instrument [Line Items]
Basis spread on variable rate	1.00%
Term Loan | Term Loan B Credit Agreement | Term Loan A | Base Rate | Variable Rate Component Two
Debt Instrument [Line Items]
Basis spread on variable rate	1.50%
Term Loan | Bridge Facility
Debt Instrument [Line Items]
Interest expense, debt		$ 3,100,000
Revolving Credit Facility
Debt Instrument [Line Items]
Long-term debt		190,000,000	122,900,000
Remaining borrowing capacity		303,500,000	$ 268,800,000
Revolving Credit Facility | Term Loan A
Debt Instrument [Line Items]
Maximum borrowing capacity		$ 500,000,000			$ 500,000,000