Segment Information - Schedule of Operating Segments (Details) - EUR (€) € in Thousands	2 Months Ended	5 Months Ended	7 Months Ended	12 Months Ended
	Apr. 30, 2021	Sep. 30, 2021	Apr. 30, 2021	Sep. 30, 2023	Sep. 30, 2022
Disclosure of operating segments [line items]
Sales		€ 462,664	€ 499,347	€ 1,491,911	€ 1,242,833
Adjusted EBITDA		140,340	152,000	482,706	434,555
Effects from applying the acquisition method of accounting for the Transaction		(110,900)			(24,367)
Transaction related advisory costs		(2,463)			(2,598)
IPO-related costs				(30,603)
Consulting fees relating to Group transformation		(1,892)			(7,982)
Other transaction effects			(3,025)
Realized and unrealized FX gains / losses		20,585	(1,523)	(36,056)	45,516
Share-based compensation				(65,394)
Other		(1,468)	(109)	(6,552)	(836)
EBITDA		44,202	147,343	344,101	444,288
Depreciation and amortization		(29,021)	(25,872)	(83,413)	(81,261)
Finance income (costs), net		(28,958)	(1,753)	(107,036)	(112,503)
Profit (loss) before tax	€ (25,130)	(13,777)	119,718	153,652	250,524
Total Reportable Segments
Disclosure of operating segments [line items]
Sales		461,775	498,382	1,486,621	1,239,551
Adjusted EBITDA		152,742	162,101	503,607	445,509
Total Reportable Segments | Americas
Disclosure of operating segments [line items]
Sales		223,110	264,883	804,690	667,387
Adjusted EBITDA		78,767	100,509	291,712	259,944
Total Reportable Segments | Europe
Disclosure of operating segments [line items]
Sales		191,226	184,066	529,507	449,131
Adjusted EBITDA		61,649	47,308	167,407	146,592
Total Reportable Segments | APMA
Disclosure of operating segments [line items]
Sales		47,439	49,433	152,424	123,033
Adjusted EBITDA		12,326	14,284	44,488	38,973
Corporate / Other
Disclosure of operating segments [line items]
Sales		889	965	5,289	3,282
Adjusted EBITDA		€ (12,402)	€ (10,101)	€ (20,901)	€ (10,954)