Before we were talking about what has happened, now you are asking a more general hypothetical question.
Mass vaccination is often used to eliminate a disease from a population. Something that does not exist, will, by definition, not evolve.
The Covid-19 vaccines are not eliminating Covid-19 from the population, yet. Covid-19 appears to most quickly evolve in cases of long covid. Basically, the body and Covid spend months fighting things out, creating a perfect environment for speedy evolution. The vaccine definitely reduces the number of long covid cases, so would (theoretically) reduce the speed of evolution.
Also we are seeing the same traits in multiple strains. This implies there are a limited number of mutations that are easy and beneficial to the virus. Evolution may have hit a dead end before the vaccine.
Obviously, this is all conjecture. All we know is there is no strains yet that can be linked to the vaccine. Whether that will hold true in the future is impossible to say. If it does continue to hold true, then it will take even longer to explain why.