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Summary of Significant Accounting Policies - Additional Information (Details)
 12 Months Ended
Sep. 30, 2023
USD ($)
reportable_unit
Sep. 30, 2022
USD ($)
Sep. 30, 2021
USD ($)
Oct. 01, 2022
USD ($)
Sep. 30, 2020
USD ($)
Concentration Risk [Line Items]          
Allowance for doubtful accounts $ 743,000 $ 590,000      
Settlement assets 4,873,000 7,540,000 $ 4,768,000   $ 0
Settlement obligations 4,873,000 7,540,000      
Inventory 4,138,000 4,121,000      
Impairment charges $ 0 0 0    
Estimated useful life 3 years        
Loss on impairment of related to an internal use software project $ 2,660,000 0 0    
Notes receivable, fair value disclosure 199,000 5,125,000      
Revenue from acquisitions 18,365,000        
Net income $ 3,350,000        
Number of reporting units | reportable_unit 5        
Write down of intangible asset $ 0 0 0    
Contract with customer, asset, before allowance for credit loss 15,131,000 9,716,000      
Capitalized contract cost, gross 4,966,000 4,185,000      
Amortization expense of intangible assets 20,539,000 17,892,000 15,830,000    
Advertising expense 3,966,000 4,028,000 2,623,000    
Equity-based compensation expense 27,878,000 26,230,000 20,860,000    
Long-term debt, less current portion and debt issuance costs, net 385,081,000 287,020,000      
Additional paid-in-capital 249,688,000 241,958,000      
Accumulated earnings (12,944,000) (23,582,000)      
Cumulative Effect, Period of Adoption, Adjustment | Accounting Standards Update 2020-06          
Concentration Risk [Line Items]          
Long-term debt, less current portion and debt issuance costs, net       $ 11,933,000  
Additional paid-in-capital       (23,382,000)  
Accumulated earnings       $ 11,449,000  
Intangible Assets, Amortization Period          
Concentration Risk [Line Items]          
Amortization expense of intangible assets $ 792,000 $ 707,000 $ 533,000    
Minimum          
Concentration Risk [Line Items]          
Maturity period of settlement assets and obligations (in years) 1 day        
Maximum          
Concentration Risk [Line Items]          
Maturity period of settlement assets and obligations (in years) 4 days