Long-Term Debt - Additional Information (Details) - USD ($) $ in Millions							12 Months Ended
		May 28, 2024	Aug. 31, 2023	Aug. 28, 2023	Apr. 22, 2022	Dec. 18, 2013	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Jun. 27, 2024
Debt Instrument [Line Items]
Debt repayments							$ 0.0	$ 459.0	$ 1,006.3
Loss on debt extinguishment	[1]						(0.6)	(8.3)	(12.6)
Debt voluntary repayment							87.3	554.5	374.4
Debt borrowings during the period							0.5	549.5	$ 391.7
Long-term debt, fair value							$ 812.4	$ 900.1
Receivables Financing Agreement | Wholly-owned Subsidiary
Debt Instrument [Line Items]
Credit agreement, maximum borrowing capacity										$ 325.0
Interest period term							6 months
Weighted average interest rate							6.70%	6.30%
Commitment fee for unused balance of facility							0.40%
Debt voluntary repayment							$ 0.5	$ 549.5
Debt borrowings during the period							$ 87.3	554.5
SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		0.50%
SOFR | Maximum | Receivables Financing Agreement | Wholly-owned Subsidiary
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate							170.00%
SOFR | Minimum | Receivables Financing Agreement | Wholly-owned Subsidiary
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate							140.00%
ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		1.50%
Series B Term Loan | SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					0.50%
Series B Term Loan | ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					1.50%
Credit Agreement | First Lien Credit Facility Term Loans
Debt Instrument [Line Items]
Credit agreement date						Dec. 18, 2013
Debt instrument, term						7 years
Credit agreement, maximum borrowing capacity						$ 1,460.0
Credit Agreement | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Debt instrument, term						5 years
Credit agreement, maximum borrowing capacity						$ 210.0
Amended Credit Agreement
Debt Instrument [Line Items]
Loss on debt extinguishment				$ (8.3)	$ (12.6)
Percentage of prepayment premium			1.00%
Percentage of principle balance used to calculate debt repayments amount of quarterly installments due							0.25%
Debt borrowings during the period				$ 450.0
Amended Credit Agreement | SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		2.50%
Amended Credit Agreement | ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate		1.50%
Amended Credit Agreement | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Debt instrument, term					5 years
Credit agreement, maximum borrowing capacity					$ 300.0
Amended Credit Agreement | Series B Term Loan
Debt Instrument [Line Items]
Debt instrument, term					7 years
Credit agreement, maximum borrowing capacity					$ 1,200.0
Debt instrument, original discount					$ 12.0
Debt repayments							$ 0.0	$ 459.0
Debt instrument, maturity date					Apr. 22, 2029
Debt instrument, effective interest rate					3.42%
Weighted average interest rate							8.20%	7.80%
Previous Revolving Credit Facility | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Credit agreement, maximum borrowing capacity					$ 260.0
Line of credit facility, amount outstanding balance							$ 0.0	$ 0.0
Letters of credits, outstanding amount							0.0	42.6
Revolving Credit Facility | SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					0.00%
Revolving Credit Facility | ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					1.00%
Revolving Credit Facility | ABR | Maximum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					1.50%
Revolving Credit Facility | ABR | Minimum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					1.00%
Revolving Credit Facility | First Lien Revolving Credit Facility
Debt Instrument [Line Items]
Debt instrument, term					5 years
Credit agreement, maximum borrowing capacity					$ 300.0
Debt repayments							$ 0.0	$ 33.5
Debt instrument, maturity date					Apr. 22, 2027
Weighted average interest rate								6.90%
Debt borrowings during the period								$ 33.5
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR | Maximum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					2.50%
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR | Minimum
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					2.00%
Revolving Credit Facility | Series B Term Loan | SOFR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					3.25%
Revolving Credit Facility | Series B Term Loan | ABR
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					2.25%

[1] Represents losses on the extinguishment of debt related to Amendments No. 6, No. 7, and No. 8 to the Credit Agreement, in the fiscal years ended September 30, 2022, 2023, and 2024 respectively, and includes accelerated amortization of deferred financing fees and original issue discount as well as fees paid to lenders and third parties.