Goodwill and Intangible Assets - Summary of Changes in Goodwill and Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Goodwill [Roll Forward]
Net balance - beginning of period	$ 378,588	$ 168,491
Acquisition	18,481	210,097
Impairment	(57,710)	0
Disposals from sales of businesses	(3,157)
Other adjustments	400
Net balance - end of period	336,602	378,588	$ 168,491
Finite-Lived Intangible Assets [Roll Forward]
Impairment	(89,700)	0
Disposals from sales of businesses	(2,642)
Amortized expense	(13,436)	(7,630)	0
Net balance - end of period	62,403
Intangible Assets Disclosure [Roll Forward]
Net balance - beginning of period	306,471	85,294
Acquisition	11,623	228,807
Impairment recorded	(89,692)
Net balance - end of period	212,324	306,471	85,294
Trade Names
Indefinite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	186,779	85,294
Acquisitions	8,800	101,485
Impairment of intangible assets, indefinite-lived	(43,016)
Disposals from sales of businesses	(2,642)
Net balance - end of period	149,921	186,779	85,294
Developed technologies
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	14,274	0
Acquisitions	0	15,457
Impairment	(8,309)
Disposals from sales of businesses	0
Amortized expense	(1,546)	(1,183)
Net balance - end of period	4,419	14,274	0
Customer Relationships
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	101,230	0
Acquisitions	0	107,490
Impairment	(38,367)
Disposals from sales of businesses	0
Amortized expense	(10,749)	(6,260)
Net balance - end of period	52,114	101,230	0
Domain Names
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	1,970	0
Acquisitions	945	2,074
Impairment	0
Disposals from sales of businesses	0
Amortized expense	(528)	(104)
Net balance - end of period	2,387	1,970	0
Internally Developed Software
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	2,218	0
Acquisitions	1,878	2,301
Impairment	0
Disposals from sales of businesses	0
Amortized expense	(613)	(83)
Net balance - end of period	$ 3,483	$ 2,218	$ 0