I don't know how it works in Europe, but here in Argentina that QR takes you to a government website that shows you a nice static page with your info and your vaccines.
If the system is similar, you can download the website(by asking a family member/friend to show you their pass), modify the html or whatever is needed with your data, and host that modified html file yourself, you would also need to make the QR code in your fake app point to your server's ip.
You can go further and buy a domain that looks similar to the government's domain.
All of these steps are very risky because there is no way to host a website and get a domain anonymously, I'm doing it myself because no one gives a shit here, but I imagine the dictatorships in Europe are more rigorous and the people validating the QR are smarter
Btw all of this is assuming the European system is almost as low budget as ours