Mutations happen due to things such as antigen drift
Other way round - genetic variation arises as a result of accumulation of mutations.
and i haven't seen anything to suggest that this process is sped up by vaccinations.
I've seen it stated somewhere that viruses can increase the rate of mutation when under immune pressure.
As a layman one could imagine that vaccinations would mean that those mutations which get round the antibodies would be selected preferentially - but the paper i linked to earlier says that the antibodies etc act to prevent intermediate stages in the development of new variants so act to reduce the likelihood of new variants developing.
Yes that is interesting - the research is quite complicated - but it appears to me that when a more infectious variant appears, of course the diversity of variants will decline. That this correlates with increasing vaccination suggests that no vaccination would keep the diversity high. That implies less rapid spread of more infectious variants.
Note also that the more rapidly the more infectious variants spread, the more they will affect unvaccinated people, hence the reason for the higher morbidity and mortality among unvaccinated is that the vaccines have accelerated spread of these variants.
What you talk about here is just as likely with natural infection as with vaccination as far as I can see - since the immunity from natural infection isn't neutralising either - and new variants formed prior to vaccinations.
Innate immunity is very effective - that;s why children and young, healthy adults were generally asymptomatic during the first wave (when the infection rate was lower, so re-infection was less likely). Adaptive immunity is also very effective, but also wanes over time. The problem is the more pressure we put on the virus, the more infectious it has to become.
I'm talking in this post about last year's VOCs, Alpha etc. As far as the less severe Omicron goes, it has been suggested that it arose when a strain similar to Wuhan jumped into mice and then evolved in them, before jumping back to humans. Something to do with mouse ACE 2... remaining questions are, did the vaccines cause that, and if so, will the overall cost to human life of everyone being infected be worth paying?