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Income Taxes - Differences Between Income Tax Provision (Benefit) and Income Taxes Computed using Applicable U.S. Statutory Federal Tax Rate (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Effective Income Tax Rate Reconciliation, Amount [Abstract] |  |  |
Income tax benefit computed at federal statutory rate | $ (6,331) | $ (2,086) | $ (10,284)
State income taxes, net of federal benefit | (851) | (776) | (1,005)
Foreign income taxed at different rates | (22) | (1,182) | (2,594)
Impact of investments in subsidiaries | (6,058) |  | 7,128
Nontaxable gain from acquisition earn-out liability reversal | (3,959) |  |
Change in deferred tax asset valuation allowance | 1,137 | 1,337 | (3,247)
Impact of change in uncertain tax positions | (1,321) | (358) | (10,607)
Global intangible low taxed income, net of foreign tax credits |  | 4,060 | 4,051
Impact of tax rate changes | (1,391) | 1,531 | 165
Compensation | 1,598 | (1,199) | 462
Tax credits | (1,434) | (2,102) | (4,050)
Merger costs | 1,056 | 1,629 | 20
Other non-deductible expenses and other taxes | 1,304 | 643 | 591
Impact of effective state tax rate change |  | 763 |
Research and development expense deduction | (1,278) | (910) | (730)
Income tax (benefit) expense | $ (17,550) | $ 1,350 | $ (20,100)

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- Definition Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to nontaxable gain from acquisition earn-out liability reversal. + References No definition available. + Details
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- Definition Amount of reported income tax expense from difference to expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operations, attributable to global intangible low-taxed income (GILTI). + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 12 -Publisher FASB -URI https://asc.fasb.org//1943274/2147482685/740-10-50-12 + Details
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