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Fair Value Measurements (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]    
Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration] Costs and Expenses Costs and Expenses
Exchangeable notes, fair value $ 108,506  
Accrued Contingent Consideration    
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]    
Balance, beginning 22,833 $ 36,229
Contingent consideration accrued at time of business combination 760 6,281
Change in fair value of contingent consideration included in Operating expenses 10,781 23,725
Contingent consideration paid (26,135) (43,402)
Balance, ending 8,239 22,833
Accrued Expenses and Other Current Liabilities    
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]    
Contingent consideration 6,825 21,385
Other Long-term Liabilities    
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]    
Contingent consideration $ 1,414 $ 1,448