There's a missing part to this by the way: you need a reservoir for new mutations to replicate in, and they have to be mutations which become dominant in the reservoir.

Since the vaccines reduced R(eff), generally below 1 (so far observed), any chain of infection through vaccinated people tends to terminate - not continue. Which means however vaccine evading that virus is, all of it dies.

This all changes if you have a large group of unvaccinated people presenting no challenge to it. Freely spreading for a whole lot of cycles through that population means more vaccine-resistant copies are now out there, with more opportunity to challenge vaccine resistant individuals they come into contact with (since R(eff) in the unvaccinated is ~8).