Accumulated Other Comprehensive Loss - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	$ 911,659	$ 958,474	$ 839,779
Total other comprehensive loss, net of tax	(489)	(2,594)	(2,535)
Ending balance	625,740	911,659	958,474
Foreign Currency Translation Adjustments
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(37,340)	(34,679)	(31,609)
Other comprehensive income (loss) before reclassifications	(338)	(2,661)	(3,070)
Income tax expense	0	0	0
Other comprehensive income (loss) before reclassifications, net of tax	(338)	(2,661)	(3,070)
Amounts reclassified from accumulated other comprehensive loss	0	0	0
Income tax expense (benefit)	0	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	0	0	0
Total other comprehensive loss, net of tax	(338)	(2,661)	(3,070)
Ending balance	(37,678)	(37,340)	(34,679)
Cash Flow Hedges, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(304)	0	0
Other comprehensive income (loss) before reclassifications	(86)	(277)	0
Income tax expense	20	62	0
Other comprehensive income (loss) before reclassifications, net of tax	(66)	(215)	0
Amounts reclassified from accumulated other comprehensive loss	(1,365)	(115)	0
Income tax expense (benefit)	307	26	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	(1,058)	(89)	0
Total other comprehensive loss, net of tax	(1,124)	(304)	0
Ending balance	(1,428)	(304)	0
Pension Obligations, net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(2,039)	(2,410)	(2,945)
Other comprehensive income (loss) before reclassifications	178	(2)	355
Income tax expense	(40)	0	(80)
Other comprehensive income (loss) before reclassifications, net of tax	138	(2)	275
Amounts reclassified from accumulated other comprehensive loss	1,078	481	336
Income tax expense (benefit)	(243)	(108)	(76)
Amounts reclassified from accumulated other comprehensive loss, net of tax	835	373	260
Total other comprehensive loss, net of tax	973	371	535
Ending balance	(1,066)	(2,039)	(2,410)
Accumulated Other Comprehensive Loss
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(39,683)	(37,089)	(34,554)
Other comprehensive income (loss) before reclassifications	(246)	(2,940)	(2,715)
Income tax expense	(20)	62	(80)
Other comprehensive income (loss) before reclassifications, net of tax	(266)	(2,878)	(2,795)
Amounts reclassified from accumulated other comprehensive loss	(287)	366	336
Income tax expense (benefit)	64	(82)	(76)
Amounts reclassified from accumulated other comprehensive loss, net of tax	(223)	284	260
Total other comprehensive loss, net of tax	(489)	(2,594)	(2,535)
Ending balance	$ (40,172)	$ (39,683)	$ (37,089)