Goodwill and Intangible Assets - (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2024	Sep. 30, 2024
Goodwill [Line Items]
Goodwill	$ 531,445	$ 538,266
Goodwill, decreased from effects of foreign currency exchange rates	7,200
Intangible assets, decreased from effects of foreign currency exchange rates	1,400
SBS
Goodwill [Line Items]
Goodwill	82,600
BSG
Goodwill [Line Items]
Goodwill	448,200
Exclusive Beauty Supply, Inc.
Goodwill [Line Items]
Goodwill adjustment related to acquisitions	$ 400