I fully expect to see proof of vaccination required for international travel. Countries will not want sick travelers adding to their problems with already overburdened domestic health care systems.
Which has long been a requirement/recommendation for travel to certain countries, but not to attend domestic events. And yes, I know states put in their own entry/exit rules with COVID. We almost went there with measles (remember?) which is far more infectious and transmissible with an R=18, I believe, with NO cure. But it became a non-issue, thankfully.
Here's the deal. I have never had to 'show' that I had certain vaccinations; nobody has asked previous to this. I've had to answer questions on forms for a new doctor, but I don't have to show any proof that I've been vaccinated for polio, for example. Healthcare professionals ask me if I've had my flu shot, I say 'Yes', and I don't have to show anything. If someone asks me if I've been vaccinated for COVID, I'll tell them the truth, i.e. 'No', 'I've had my first shot', 'I've had my second shot', and 'I'm two weeks out from my second shot'.
So my example still stands: No one asks for my ID when I vote, so again, I expect to be believed if I tell someone I've been vaccinated.