Equity - Additional Information (Details) € / shares in Units, $ / shares in Units, € in Thousands, $ in Millions							12 Months Ended
	May 30, 2025 EUR (€) shares	May 30, 2025 $ / shares shares	Jul. 03, 2024 $ / shares shares	Oct. 13, 2023 EUR (€) shares	Oct. 13, 2023 USD ($) $ / shares shares	Oct. 10, 2023 shares	Sep. 30, 2025 EUR (€) shares	Sep. 30, 2024 EUR (€) shares	Jun. 28, 2024 $ / shares shares	Oct. 02, 2023 € / shares shares	Sep. 30, 2023 shares	Sep. 30, 2022 shares
Disclosure Of Detailed Information About Equity [line items]
Total proceeds from IPO | €								€ 449,214
Ordinary Shares
Disclosure Of Detailed Information About Equity [line items]
Number of ordinary shares | shares				187,825,592	187,825,592		183,906,056	187,829,202		182,721,369	182,721,369	182,721,369
Ordinary Shares, Secondary Offering
Disclosure Of Detailed Information About Equity [line items]
Shares issued | shares		16,100,000	16,100,000
Number of shares exercised, option to purchase additional shares | shares		2,100,000	2,100,000
Ordinary shares at a price | $ / shares		$ 52.5	$ 54
Ordinary share price | $ / shares		$ 52.5							$ 54
Costs incurred | €	€ 1,700						€ 1,900
Ordinary Shares, Secondary Offering | MidCo
Disclosure Of Detailed Information About Equity [line items]
Shares issued | shares		14,000,000							14,000,000
Ordinary Shares
Disclosure Of Detailed Information About Equity [line items]
Description of no par value ordinary shares							Prior to the IPO, the Company completed a capital reorganization. On October 2, 2023, the Company converted its share capital, comprised of 182,721,369 ordinary shares of €1.00 par value into 182,721,369 no par value ordinary shares.
Shares repurchased of ordinary shares | shares	3,927,344					5,648,465	3,927,344
Shares issued | shares				10,752,688	10,752,688
Initial public offering price | $ / shares					$ 46
Total proceeds from IPO				€ 450,000	$ 473.6
Early repayment of borrowings | €				100,000
Ordinary share price | $ / shares		$ 50.925
Par value per share | € / shares										€ 1
Shares repurchased amount of ordinary shares | €							€ 176,400
Initial Public Offering
Disclosure Of Detailed Information About Equity [line items]
Underwriting commission fees | €				19,800
Deferred offering costs | €				3,000
USD Term Loan | Ordinary Shares
Disclosure Of Detailed Information About Equity [line items]
Early repayment of borrowings				€ 423,800	$ 450.0