It’s the pool of the unvaccinated that is the variant factory. Aided by whoever started this bioweapon in the first place.
I think that the more likely scenario is the opposite. Vaccinated people have an artificially introduced agent that attacks the original virus construction (I guess called 'alpha' Covid), thus this will drive mutations of different variations of the alpha Covid (e.g., beta, gamma, delta, etc). The original alpha Covid would just go after the un-vaccinated. And I'd suspect that the un-vaccinated survivors (99.9% of those exposed to the virus) would have a broader set of anti-bodies that could handle the variants better than those that were loaded up with artificial antibodies.