European Vaccination Passport

There are, literally, dozens of posts here about the subject. You could start with the FAQs page, too.
https://www.ricksteves.com/tours/coronavirus-faq

If, like me, you plan to travel with RS next year, my suggestion is to wait a while, as things will undoubtedly change. I also expect to get pertinent info from RS before my tour.

Essentially, there is no European Vaccination Passport. Each country issues it's own form of a "green pass", though one issued by one country will be honored by another EU country.

Policies regarding issuing the countries Green pass to non-residents varies. France will allow you to get one, and you can apply and receive it before going. The Netherlands and Italy will not issue a pass to non-residents, but Italy honors your CDC card, the Netherlands however will not.

Basically, you need to look into how passes are handled in each country you will be in.

Each country issues the "Green Pass" based on how their countries medical system works. In Germany, for example, the pharmacy or doctors office that performed the vaccination issues the pass. In Italy I believe the individual gets an email with a link from the health system. There is a mechanism for a tourist from the US to request a pass in France; people have had varying degrees of luck getting them.

All the EU "Green Passes" are based on a common specification and various countries honor passes issued in other countries.

The UK has their own pass, issued by the NHS.

No US state, to my knowledge, can issue an EU "Green Pass." Some states are issuing a "Smart Health Card" QR code showing vaccination/test/recovery status, but those passes are not the same. (I've dug into the actual software specifications for the EU pass and the "Smart Health Card" being issued various places in the US.)

My mom, sister and brother-in-law went to France in September and applied for the vaccination passport a week or so before they left. They were there for nearly three weeks and finally got their vaccination passports a few days before returning home! Fortunately, most restaurants were willing to accept their CDC cards. Hopefully, there will be better systems in place by next year!