Segment Data and Foreign Operations - Revenue and Assets (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2023	May 31, 2022	May 31, 2023	May 31, 2022	Aug. 31, 2022
Concentration risk
Revenue	$ 106,645	$ 88,619	$ 303,818	$ 237,582
Property, plant and equipment, net	61,918		61,918		$ 24,248
Goodwill and Intangible assets, less accumulated amortization	341,690		341,690		128,821
United States
Concentration risk
Revenue	92,061	76,140	259,807	204,009
Property, plant and equipment, net	58,950		58,950		21,300
Goodwill and Intangible assets, less accumulated amortization	307,636		307,636		105,216
United Kingdom
Concentration risk
Revenue	5,995	6,604	17,304	17,125
Property, plant and equipment, net	1,786		1,786		1,832
Goodwill and Intangible assets, less accumulated amortization	3,516		3,516		3,318
France
Concentration risk
Revenue	5,795	2,667	18,906	7,638
Property, plant and equipment, net	314		314		239
Goodwill and Intangible assets, less accumulated amortization	29,885		29,885		20,130
All other Foreign
Concentration risk
Revenue	2,794	$ 3,208	7,801	$ 8,810
Property, plant and equipment, net	868		868		877
Goodwill and Intangible assets, less accumulated amortization	$ 653		$ 653		$ 157