Accumulated Other Comprehensive Loss - Schedule of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2024	May 31, 2023
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	$ 847,466	$ 928,438	$ 911,659	$ 958,474
Total other comprehensive income (loss), net of tax	616	420	615	(3,096)
Ending balance	646,025	939,592	646,025	939,592
Foreign Currency Translation Adjustments
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(37,922)	(38,286)	(37,340)	(34,679)
Other comprehensive (loss) income before reclassifications	(308)	362	(890)	(3,245)
Income tax (expense) benefit	0	0	0	0
Other comprehensive (loss) income before reclassifications, net of tax	(308)	362	(890)	(3,245)
Amounts reclassified from accumulated other comprehensive loss	0	0	0	0
Income tax expense (benefit)	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss, net of tax	0	0	0	0
Total other comprehensive income (loss), net of tax	(308)	362	(890)	(3,245)
Ending balance	(38,230)	(37,924)	(38,230)	(37,924)
Cash Flow Hedges, Net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(126)		(304)
Other comprehensive (loss) income before reclassifications	1,346		2,254
Income tax (expense) benefit	(303)		(507)
Other comprehensive (loss) income before reclassifications, net of tax	1,043		1,747
Amounts reclassified from accumulated other comprehensive loss	(344)		(1,023)
Income tax expense (benefit)	77		230
Amounts reclassified from accumulated other comprehensive loss, net of tax	(267)		(793)
Total other comprehensive income (loss), net of tax	776		954
Ending balance	650		650
Pension Obligations, Net
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(1,636)	(2,319)	(2,039)	(2,410)
Other comprehensive (loss) income before reclassifications	0	0	178	(34)
Income tax (expense) benefit	0	0	(40)	8
Other comprehensive (loss) income before reclassifications, net of tax	0	0	138	(26)
Amounts reclassified from accumulated other comprehensive loss	191	75	533	226
Income tax expense (benefit)	(43)	(17)	(120)	(51)
Amounts reclassified from accumulated other comprehensive loss, net of tax	148	58	413	175
Total other comprehensive income (loss), net of tax	148	58	551	149
Ending balance	(1,488)	(2,261)	(1,488)	(2,261)
Accumulated Other Comprehensive Loss
Increase (Decrease) In Accumulated Other Comprehensive Loss [Roll Forward]
Beginning balance	(39,684)	(40,605)	(39,683)	(37,089)
Other comprehensive (loss) income before reclassifications	1,038	362	1,542	(3,279)
Income tax (expense) benefit	(303)	0	(547)	8
Other comprehensive (loss) income before reclassifications, net of tax	735	362	995	(3,271)
Amounts reclassified from accumulated other comprehensive loss	(153)	75	(490)	226
Income tax expense (benefit)	34	(17)	110	(51)
Amounts reclassified from accumulated other comprehensive loss, net of tax	(119)	58	(380)	175
Total other comprehensive income (loss), net of tax	616	420	615	(3,096)
Ending balance	$ (39,068)	$ (40,185)	$ (39,068)	$ (40,185)