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Goodwill and Intangible Assets - Changes in Carrying Amount of Goodwill (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Goodwill and Intangible Assets Disclosure [Abstract]    
Balance $ 890,802 $ 1,128,511
Goodwill impairment   (213,720)
Effect of foreign currency translation 9,540 (23,989)
Balance $ 900,342 $ 890,802