Goodwill and Intangible Assets - Summary of Changes in Goodwill and Identifiable Intangible Assets (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Goodwill [Roll Forward]
Net balance - beginning of period	$ 336,602	$ 378,588
Acquisition	0	18,481
Impairment	0	(57,710)
Disposals from sales of businesses		(3,157)
Other adjustments		400
Net balance - end of period	336,602	336,602	$ 378,588
Indefinite-Lived Intangible Assets [Roll Forward]
Impairment of intangible assets, indefinite-lived	0	(43,000)
Restructuring and impairment	0	57,710
Impairment of intangible assets, finite-lived	0	46,700
Impairment recorded		89,692
Disposals from sales of businesses		3,157
Disposals from sales of businesses		2,642
Other adjustments		$ 400
Impairment, Intangible Asset, Statement of Income or Comprehensive Income [Extensible Enumeration]		Restructuring and impairment
Finite-Lived Intangible Assets [Roll Forward]
Impairment	0	$ (46,700)
Disposals from sales of businesses		(2,642)
Amortized expense	(7,842)	(13,436)	(7,600)
Net balance - end of period	55,470
Intangible Assets Disclosure [Roll Forward]
Net balance - beginning of period	212,324	306,471
Acquisition	909	11,623
Impairment recorded		(89,692)
Net balance - end of period	205,391	212,324	306,471
Trade Names
Indefinite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	149,921	186,779
Acquisitions	0	8,800
Impairment of intangible assets, indefinite-lived		(43,016)
Disposals from sales of businesses		(2,642)
Net balance - end of period	149,921	149,921	186,779
Developed Technologies
Indefinite-Lived Intangible Assets [Roll Forward]
Impairment of intangible assets, finite-lived		8,309
Disposals from sales of businesses		0
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	4,419	14,274
Acquisitions	0	0
Impairment		(8,309)
Disposals from sales of businesses		0
Amortized expense	(455)	(1,546)
Net balance - end of period	3,964	4,419	14,274
Customer Relationships
Indefinite-Lived Intangible Assets [Roll Forward]
Impairment of intangible assets, finite-lived		38,367
Disposals from sales of businesses		0
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	52,114	101,230
Acquisitions	0	0
Impairment		(38,367)
Disposals from sales of businesses		0
Amortized expense	(5,711)	(10,749)
Net balance - end of period	46,403	52,114	101,230
Domain Names
Indefinite-Lived Intangible Assets [Roll Forward]
Impairment of intangible assets, finite-lived		0
Disposals from sales of businesses		0
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	2,387	1,970
Acquisitions	0	945
Impairment		0
Disposals from sales of businesses		0
Amortized expense	(637)	(528)
Net balance - end of period	1,750	2,387	1,970
Internally Developed Software
Indefinite-Lived Intangible Assets [Roll Forward]
Impairment of intangible assets, finite-lived		0
Disposals from sales of businesses		0
Finite-Lived Intangible Assets [Roll Forward]
Net balance - beginning of period	3,483	2,218
Acquisitions	909	1,878
Impairment		0
Disposals from sales of businesses		0
Amortized expense	(1,039)	(613)	(100)
Net balance - end of period	$ 3,353	$ 3,483	$ 2,218