I wonder what is the mutation mode of viruses regarding vaccines? Does harsher environment (more people with immunity) spur mutation, or is mutation frequency correlating with number of infected people?
The latter. Vaccines just affect the pathway variants take, but not the rate at which they mutate (they aren't bacteria and other life forms). And argument can be made that the vaccines create pathways to variants that wouldn't have been as viable without the existence of the vaccine, but that's relatively academic. A large population is what increases variant creation.