Income Taxes - Deferred Tax Assets (Liabilities) (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Sep. 30, 2021
Deferred tax assets:
Deferred Tax Assets, Operating Loss Carryforwards, Foreign	$ 8,800
Contract assets and costs	91,298	$ 0
Deferred Tax Assets, Deferred Income	11,783	0
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Other	23,429	3,525
Deferred Tax Assets, Goodwill and Intangible Assets	21,694	17,863
Deferred Tax Assets, Property, Plant and Equipment	5,135	0
Deferred Tax Assets, Other	3,615	3,555
Deferred tax assets, total	87,375	52,556
Components of Deferred Tax Liabilities [Abstract]
Deferred revenue	(1,092)	(2,404)
Deferred Tax Liabilities, Property, Plant and Equipment	(7,634)	(2,087)
Deferred Tax Liabilities, Other	(4,180)	(2,710)
Deferred Tax Liabilities, Intangible Assets	(1,099,532)	(172,551)
Deferred tax liabilities, gross	(1,203,736)	(179,752)
Deferred tax liabilities, total	(1,140,471)	(141,786)
Deferred Tax Assets, Valuation Allowance	(24,110)	(14,590)
Deferred Tax Assets, Net, Noncurrent	63,265	37,966
Deferred Tax Assets, Operating Loss Carryforwards	11,557	14,442
Deferred Tax Assets, Tax Credit Carryforwards	$ 10,162	$ 13,171