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Goodwill and Other Intangible Assets - Summary of Gross Carrying Amounts and Accumulated Amortization of Intangible Assets by Major Class (Details) - USD ($) $ in Thousands | 6 Months Ended | 12 Months Ended
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Mar. 31, 2023 | Sep. 30, 2022
Finite Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 197,665 | $ 193,098
Accumulated Amortization | (192,366) | (183,398)
Net Carrying Amount | 5,299 | 9,700
Customer Relationships |  |
Finite Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 107,913 | 104,498
Accumulated Amortization | (102,925) | (95,315)
Net Carrying Amount | $ 4,988 | $ 9,183
Weighted Average Remaining Life (Years) | 2 years | 1 year 8 months 12 days
Technology and Patents |  |
Finite Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 89,752 | $ 88,600
Accumulated Amortization | (89,441) | (88,083)
Net Carrying Amount | $ 311 | $ 517
Weighted Average Remaining Life (Years) | 8 months 12 days | 1 year 2 months 12 days

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