Summary of Significant Accounting Policies (Details)	12 Months Ended
	Sep. 30, 2022 USD ($) reportable_unit	Sep. 30, 2021 USD ($)	Sep. 30, 2020 USD ($)	Oct. 01, 2022 USD ($)	Sep. 30, 2019 USD ($)
Concentration Risk [Line Items]
Allowance for doubtful accounts	$ 590,000	$ 181,000
Settlement assets	7,540,000	4,768,000	$ 0		$ 0
Settlement obligations	7,540,000	4,768,000
Inventory	4,121,000	2,220,000
Impairment charges	$ 0	0	0
Estimated useful life	3 years
Notes receivable, fair value disclosure	$ 5,125,000	4,695,000
Revenue from acquisitions	35,840,000
Net income	5,170,000
Goodwill impairment	$ 0	0	0
Number of reporting units | reportable_unit	5
Impairment of intangible assets, excluding goodwill	$ 0	0	0
Contract with customer, asset, before allowance for credit loss	9,716,000	1,505,000
Capitalized contract cost, gross	4,185,000	3,851,000
Amortization expense of intangible assets	17,892,000	15,830,000	12,414,000
Advertising expense	4,028,000	2,623,000	1,813,000
Equity-based compensation expense	26,230,000	20,860,000	10,452,000
Reduction in income tax expense	(5,007,000)	(623,000)	2,795,000
Long-term debt, less current portion and debt issuance costs, net	287,020,000	200,605,000
Additional paid-in-capital	241,958,000	211,237,000
Accumulated earnings	(23,582,000)	(6,480,000)
Cumulative Effect, Period of Adoption, Adjustment | Accounting Standards Update 2020-06 | Subsequent Event
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
Class B Common Stock
Concentration Risk [Line Items]
Reduction in the benefit from income taxes			235,000
Increase to net loss			3,728,000
Reduction in company's net loss			3,493,000
Intangible Assets, Amortization Period
Concentration Risk [Line Items]
Amortization expense of intangible assets	$ 707,000	$ 533,000	398,000
Change in Accounting Method Accounted for as Change in Estimate
Concentration Risk [Line Items]
Change in valuation allowance for deferred tax assets			2,668,000
Reduction in income tax expense			$ 2,668,000
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