Operating Expenses - Additional Information (Details) € in Thousands, $ in Millions	5 Months Ended	7 Months Ended	12 Months Ended
	Sep. 30, 2021 EUR (€)	Apr. 30, 2021 EUR (€)	Sep. 30, 2023 EUR (€)	Sep. 30, 2023 USD ($)	Sep. 30, 2022 EUR (€)	Sep. 30, 2022 USD ($)
Senior Leadership Team
Disclosure of attribution of expenses by nature to their function [line items]
Deferred compensation plan contribution amount | €			€ 54,752
German Govermental Plan
Disclosure of attribution of expenses by nature to their function [line items]
Employers contribution to pension plan percent			9.30%	9.30%
Employers contribution to pension plan amount | €			€ 15,000		€ 12,300
Safe Harbor 401(K) Contribution (US)
Disclosure of attribution of expenses by nature to their function [line items]
Employers contribution to pension plan percent			5.00%	5.00%
Employers contribution to pension plan amount | $				$ 1.1		$ 0.9
Profit Share (US)
Disclosure of attribution of expenses by nature to their function [line items]
Employers contribution to pension plan percent			8.00%	8.00%
Employers contribution to pension plan amount | $				$ 0.2		0.2
Non-Qualified Deferred Compensation Plan (NQDCP) (US)
Disclosure of attribution of expenses by nature to their function [line items]
Deferred compensation plan contribution percentage			7.00%	7.00%
Deferred compensation plan contribution amount | $				$ 0.4		$ 0.6
Non-Qualified Deferred Compensation Plan (NQDCP) (US) | Senior Leadership Team
Disclosure of attribution of expenses by nature to their function [line items]
Deferred compensation plan contribution percentage			20.00%	20.00%
Percentage of bonus payment			20.00%	20.00%
Selling and Distribution Expenses
Disclosure of attribution of expenses by nature to their function [line items]
Shipping and handling costs | €	€ 33,200	€ 34,500	€ 155,200		€ 101,100