Fair Value Measurement - Additional Information (Details) - EUR (€)	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024
Disclosure of fair value measurement [abstract]
Transfers out of level 1 into level 2 of fair value hierarchy, liabilities held at end of reporting period	€ 0	€ 0
Transfers out of level 2 into level 1 of fair value hierarchy, liabilities held at end of reporting period	0	0
Tax receivable agreement liability	302,400,000	344,590,000
Increase (decrease) in fair value recorded through Finance cost, net	€ (9,800,000)	€ 3,800,000
Percentage of yield volatility	35.00%	40.00%
Percentage of credit spread	1.24%	1.13%
Percentge of increase decrease in yield volatility	2.50%	2.50%
Increase/decrease in fair value	€ 900,000	€ 1,200,000
Cash flow hedge reserve of a cumulative loss		€ 300,000