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Summary of Significant Accounting Policies - Foreign Currency Translation (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Gain (Loss), Foreign Currency Transaction, before Tax [Abstract] |  |  |
Foreign currency transaction and remeasurement gains (losses) | $ 4,200 | $ 1,700 | $ 1,800
Foreign currency translation reclassification adjustments included in income from discontinued operations |  | $ (16,567) |

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