[AntiImperialis2]

>Why would vaccination increase the likelihood of new mutations, or mutations surviving better?

Our immune systems are general enough to face a wide variety of viruses, infections and strains.

When one is vaccinated, it gets prepared for that particular strain of a particular virus. The cost is that it could become more vulnerable to other infections... it's the cost/benefit of specialization vs generalization. Reference: https://pubmed.ncbi.nlm.nih.gov/14970928/

The reason is that the immune system is highly optimized and it is optimized to be flexible enough to save enough individuals for the next generation. It is not optimized to save each and every individual against all possible infections. That is unnecessary, as far as evolution is concerned.

Having said that, vaccines generally don't weaken individuals to a slightly different variant of the same virus. It should rather strengthen it. The immune system expects the virus to mutate so it prepares for the mutations to an extent. In fact, a category of vaccines called live-attenuated vaccines are basically weakened strains of the same virus (these can sometimes mutate into dangerous strains, eg. https://www.the-scientist.com/news-opinion/polio-vaccination..., but that's a different discussion).