Yes. Zitadel is free or has a free plan, according to the pricing each company publishes. Free plans usually carry limits; each product page links to the company's terms.
Which European authentication tools are open source?
privacyIDEA, Rauthy and Zitadel publish their source code under an open-source licence. Each product page shows the licence and where the code is.
Which European authentication tools can you host yourself?
privacyIDEA, Bare.ID, Rauthy and Zitadel can be run on your own servers, according to their own documentation.