Related Party - Additional Information (Details) $ in Millions	1 Months Ended				3 Months Ended		9 Months Ended
	Jul. 31, 2024 EUR (€)	Jul. 31, 2024 USD ($)	Dec. 31, 2023 EUR (€)	Dec. 31, 2023 USD ($)	Jun. 30, 2024 EUR (€) shares	Jun. 30, 2023 EUR (€)	Jun. 30, 2024 EUR (€) shares	Jun. 30, 2023 EUR (€)	Sep. 30, 2023 EUR (€)
Disclosure of transactions between related parties [line items]
Right of use Assets					€ 162,929,000		€ 162,929,000		€ 122,984,000
Ockenfels
Disclosure of transactions between related parties [line items]
Lease payments					200,000	€ 200,000	400,000	€ 400,000
Lease liability					1,400,000		1,400,000		1,700,000
Right of use Assets					1,400,000		1,400,000		1,700,000
Outstanding receivables					5,500,000		5,500,000		2,500,000
Management Investment Plan
Disclosure of transactions between related parties [line items]
Paid personal income taxes for the fully vested program			€ 11,400,000	$ 12.6
Events After Reporting Period
Disclosure of transactions between related parties [line items]
Receivable partially paid back amount	€ 7,100,000	$ 7.6
Other related parties [member]
Disclosure of transactions between related parties [line items]
Marketing expenses					0	0	100,000	100,000
Lease liability					200,000		200,000		100,000
Right of use Assets					200,000		200,000		€ 100,000
Consulting fees and cost reimbursements					100,000	0	400,000	100,000
Cash Compensation					100,000		100,000
TRA liability					353,600,000		353,600,000
Director compensation					€ 100,000	€ 0	€ 200,000	€ 0
Shares issued \| shares					3,610		3,610