Dream on if you think U.S. state governments are going to give foreign governments access to their records so you can take a Rick Steves tour. Its not going to happen. A good hacker, given this type of access, can then go in to any computer in the government it wants. Its almost like giving them a key to the front door.
Remember, it's not just Americans who want to travel in Europe: Canadians, Japanese, Chinese, Africans, other Asians, Aussies, Kiwis, etc. etc etc. Are all of these countries going to open their computers up to every EU country? And remember, information can flow both ways.
What the EU might do is come up with a a "Tourist" Green card/Covid Certificate. Anyone from outside the EU, will fill out a form online that will then generate some type of QR code. A website, an app or even a printed form that could be handed in upon arrival. Something like what they are setting up for ETIAS but more Covid related.
I know what you are thinking......that could be faked. Everything could be faked.