Income Taxes - Income Tax Expense (Benefit) (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Income Tax Expense (Benefit), Continuing Operations [Abstract]
Income tax expense (benefit)	$ (260)	$ (3,260)	$ (450)	$ (7,900)
Income tax expense valuation allowance recorded against deferred tax assets in a foreign subsidiary	1,700
Income tax expense for tax deductions that are lower than the associated book compensation expense	500
Income tax expense related to a valuation allowance on beginning of year deferred tax assets	700
Income tax expense related to a valuation allowance recorded against the current year deferred tax assets	$ 5,700		$ 8,300
Deferred tax benefit resulting from the extension of a tax incentive in China				1,400
Pre-tax income not subject to income taxes				$ 17,100