Share-based Compensation - Additional Information (Details) - Management Investment Plan	1 Months Ended	12 Months Ended
	Mar. 31, 2023 shares Tranche € / shares	Sep. 30, 2025 EUR (€)	Sep. 30, 2024 EUR (€)	Sep. 30, 2023 EUR (€)
Disclosure of terms and conditions of share-based payment arrangement [line items]
Recognized share-based compensation expense		€ 0
BK LC Manco GmbH & Co. KG
Disclosure of terms and conditions of share-based payment arrangement [line items]
Number of shares granted | shares	1,197,100
Number of tranches | Tranche	5
Percentage of shares granted to each tranche	20.00%
Granted shares vesting period	4 years
Percentage of shares granted to vest after each year of service	20.00%
Percentage of shares granted that vesting with occurrence of an exit	20.00%
Minimum required period for exit event to occur after the grant	12 months
Weighted average fair value of the awards granted | € / shares	€ 57.57
Ordinary redeemable share price | € / shares	€ 72.23
BK LC Manco GmbH & Co. KG | First Tranche
Disclosure of terms and conditions of share-based payment arrangement [line items]
Percentage of grants included in grant date fair value, accounted after occurrence of exit event	20.00%
Selling and Distribution Expenses
Disclosure of terms and conditions of share-based payment arrangement [line items]
Recognized share-based compensation expense			€ 400,000	€ 7,400,000
General and Administrative Expenses
Disclosure of terms and conditions of share-based payment arrangement [line items]
Recognized share-based compensation expense			€ 3,200,000	€ 58,000,000