
Resolve has a deflicker filter (not sure if it's in the free version) which might fix the flicker issue. You could also, of course, color grade better.
But it's terribly low resolution and noisy and even if you purchase a fancy third-party AI-based filter I don't see the faces being filled in very well. Resolve doesn't have anything built-in to fix something so bad. (The Studio version has an upscaling mechanism that uses AI and can upscale fairly well, but it isn't as miraculous as what you need.)
Personally, it feels like leaving it as a historical-looking video would be a good route to take. (Again, maybe fix the flicker if you can, and maybe tweak the color grading to try to make different clips more consistent with each other.)