If one or two people don't return to restaurants as they don't want to sit amongst the unvaccinated, more room for everyone else, there's going to be a stampede of people wanting to spend money, holiday, party, go out drinking, or just enjoy family activities like theme parks.
Vaccination 'passports' are difficult to operate and could easily be forged, even if electronic. Only worth it perhaps at the border. I think places may prefer to do quick covid tests on the door than worry about trying to authenticate passports. The thing is, you can't see if someone is vaccinated, you can't even see if they are vaccinated for many things, flu, BCG, MMR, you can't tell and unless you spend your whole life asking the bus driver, all the passengers, all the other people in the restaurant, then you won't be able to know who is vaccinated.
I haven't downloaded the Track and Trace app (didn't want to, data protection) and I've never been refused anywhere, I just walk in (when not in lockdown). I will get vaccinated, but no-one will check. These businesses are crying out for customers, they aren't going to make it an unpleasant and confrontational experience with their customers to access services once the immediate risk dies down.