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Nature of Business and Summary of Significant Accounting Policies - Additional Information (Details) - USD ($) $ in Millions | 12 Months Ended
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Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Accounting Policies [Abstract] |  |  |
Depreciation and amortization, property and equipment | $ 15.2 | $ 20.3 | $ 23.5
Foreign exchange gains (losses) | 1.9 | 0.0 | (1.0)
Advertising and promotion costs | $ 8.1 | $ 6.9 | $ 8.7

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