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Significant Non-cash Transactions (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]      
Restricted Class A common stock issued as part of acquisition purchase consideration (Note 4) $ 2,000 $ 0 $ 35,245
Acquisition date fair value of contingent consideration in connection with business combinations 760 6,281 22,577
Residual buyouts financed through principal and interest forgiveness of a loan 5,860 0 0
Replacement of the Prior Senior Secured Credit Facility with the 2023 Senior Secured Credit Facility 284,000 0 0
Debt issuance costs financed with proceeds from the 2023 Senior Secured Credit Facility 2,386 0 0
Accrued interest financed with proceeds from the 2023 Senior Secured Credit Facility 1,617 0 0
Right-of-use assets obtained in exchange for operating lease obligations $ 927 $ 7,846 $ 16,879