Accumulated Other Comprehensive Loss - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	$ 958,474	$ 839,779	$ 680,436
Total other comprehensive (loss) income, net of tax	(2,594)	(2,535)	2,317
Ending balance	911,659	958,474	839,779
Foreign Currency Translation Adjustments
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(34,679)	(31,609)	(34,184)
Other comprehensive income (loss) before reclassifications	(2,661)	(3,070)	2,575
Income tax (expense) benefit	0	0	0
Other comprehensive income (loss) before reclassifications, net of tax	(2,661)	(3,070)	2,575
Amounts reclassified from accumulated other comprehensive loss	0	0	0
Income tax benefit	0	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	0	0	0
Total other comprehensive (loss) income, net of tax	(2,661)	(3,070)	2,575
Ending balance	(37,340)	(34,679)	(31,609)
Cash Flow Hedges, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	0	0	0
Other comprehensive income (loss) before reclassifications	(277)	0	0
Income tax (expense) benefit	62	0	0
Other comprehensive income (loss) before reclassifications, net of tax	(215)	0	0
Amounts reclassified from accumulated other comprehensive loss	(115)	0	0
Income tax benefit	26	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	(89)	0	0
Total other comprehensive (loss) income, net of tax	(304)	0	0
Ending balance	(304)	0	0
Pension Obligations, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(2,410)	(2,945)	(2,687)
Other comprehensive income (loss) before reclassifications	(2)	355	(530)
Income tax (expense) benefit	0	(80)	120
Other comprehensive income (loss) before reclassifications, net of tax	(2)	275	(410)
Amounts reclassified from accumulated other comprehensive loss	481	336	196
Income tax benefit	(108)	(76)	(44)
Amounts reclassified from accumulated other comprehensive loss, net of tax	373	260	152
Total other comprehensive (loss) income, net of tax	371	535	(258)
Ending balance	(2,039)	(2,410)	(2,945)
Accumulated Other Comprehensive Loss
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(37,089)	(34,554)	(36,871)
Other comprehensive income (loss) before reclassifications	(2,940)	(2,715)	2,045
Income tax (expense) benefit	62	(80)	120
Other comprehensive income (loss) before reclassifications, net of tax	(2,878)	(2,795)	2,165
Amounts reclassified from accumulated other comprehensive loss	366	336	196
Income tax benefit	(82)	(76)	(44)
Amounts reclassified from accumulated other comprehensive loss, net of tax	284	260	152
Total other comprehensive (loss) income, net of tax	(2,594)	(2,535)	2,317
Ending balance	$ (39,683)	$ (37,089)	$ (34,554)