I have no background in molecular biology but this is a question that I've been asking myself. I've read that variants emerge the longer a virus is incubated in the body - most likely from COVID "long haulers" who have trouble clearing the infection. With the rollout of vaccines like Johnson and Johnson and Astra Zeneca, the vaccine is at very effective at preventing severe disease and death, but less affective at preventing mild disease and I'm guessing asymptomatic infection.

So, my question: is there a scenario where these moderately effective vaccines lead to more dangerous mutations (which will render existing vaccines useless), as the virus has more opportunity to "hang around" in the body? Or is my understanding totally false?