Tax Receivable Agreement - Additional Information (Details) € in Thousands, $ in Millions				12 Months Ended
	May 30, 2025 shares	Oct. 10, 2023 EUR (€) shares	Oct. 10, 2023 USD ($) shares	Sep. 30, 2025 EUR (€) shares	Sep. 30, 2025 USD ($) shares	Sep. 30, 2024 EUR (€)
Tax Receivable Agreement [Line Items]
Payments to the tax receivable agreement (tra)		85.00%	85.00%
Benefit of the remaining applicable tax savings		15.00%	15.00%
Future payments expected to be made under Tax Receivable Agreement		€ 298,900	$ 239.4
Future expected period of payment to be made under tax receivable agreement		12 years	12 years
Estimate of expected future undiscounted cash payments				€ 273,400	$ 236.1
TRA liability current				54,364		€ 15,300
Carrying Value
Tax Receivable Agreement [Line Items]
TRA liability				356,800		359,900
TRA liability current				€ 54,400		€ 15,300
Level 3 \| Fair Value
Tax Receivable Agreement [Line Items]
TRA liability		€ 355,800
Ordinary Shares
Tax Receivable Agreement [Line Items]
Shares repurchased of ordinary shares \| shares	3,927,344	5,648,465	5,648,465	3,927,344	3,927,344