Goodwill and Other Intangible Assets, Net - Schedule of Gross Change in Carrying Amount of Goodwill (Details) - USD ($)	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Goodwill [Roll Forward]
Goodwill, beginning of period	$ 255,198,000	$ 170,304,000
Additions	14,759,000	84,040,000
Measurement period adjustments	(725,000)	1,657,000
Impairments	(39,270,000)	0	$ 0
Foreign currency translation adjustment	(543,000)	(803,000)
Goodwill, end of period	$ 229,419,000	$ 255,198,000	$ 170,304,000