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Reportable Segment Information - Geographic Revenue and Long-lived Assets (Detail) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
U.S. [Member] |  |  |
Revenues from External Customers and Long-Lived Assets [Line Items] |  |  |
Long-lived assets, net | $ 23,525 | $ 24,788 |
Ireland [Member] |  |  |
Revenues from External Customers and Long-Lived Assets [Line Items] |  |  |
Long-lived assets, net | $ 28,707 | $ 30,505 |
Revenue [Member] | Geographic Concentration Risk [Member] | Domestic [Member] |  |  |
Revenues from External Customers and Long-Lived Assets [Line Items] |  |  |
Percentage of consolidated revenue | 82.00% | 74.00% | 79.00%
Revenue [Member] | Geographic Concentration Risk [Member] | Foreign [Member] |  |  |
Revenues from External Customers and Long-Lived Assets [Line Items] |  |  |
Percentage of consolidated revenue | 18.00% | 26.00% | 21.00%

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