Fair Value Measurement - Schedule of Fair Value and Fair Value Hierarchy of Loans and Borrowings Carried at Amortized Cost (Details) - EUR (€) € in Thousands	Sep. 30, 2023	Sep. 30, 2022
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	€ 1,840,567
Level 2 | Vendor Loan
Disclosure of fair value measurement of liabilities [line items]
Nominal value	299,560	€ 287,018
Level 2 | Senior Notes
Disclosure of fair value measurement of liabilities [line items]
Nominal value	428,500	428,500
Level 2 | EUR | Term Loan
Disclosure of fair value measurement of liabilities [line items]
Nominal value	375,000	375,000
Level 2 | USD | Term Loan
Disclosure of fair value measurement of liabilities [line items]
Nominal value	781,315	860,854
Fair Value | Level 2 | Vendor Loan
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	235,687	185,783
Fair Value | Level 2 | Senior Notes
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	373,682	328,816
Fair Value | Level 2 | EUR | Term Loan
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	348,426	294,461
Fair Value | Level 2 | USD | Term Loan
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	694,889	719,761
Carrying Value | Level 2 | Vendor Loan
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	305,048	292,275
Carrying Value | Level 2 | Senior Notes
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	448,434	449,698
Carrying Value | Level 2 | EUR | Term Loan
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	368,701	367,193
Carrying Value | Level 2 | USD | Term Loan
Disclosure of fair value measurement of liabilities [line items]
Loans and borrowings	€ 730,855	€ 856,505