Hey kart_brrr, your kart frame is not the worst I have seen, BY FAR. I mean it’s pretty decent looking (from 10 feet away, lol). I looked at the photos and the only thing that really stands out to me is behind the seat on the left and those large unpainted steel parts: the custom brake caliper holder and the engine/chain guard. Those could be wire wheeled, mechanically sanded with a flap disc, etc and primered and painted with a few coats of cheap spray enamel.... You could either color match those parts to the new chassis color or paint them black or whatever you want.
There’s rust on other minor parts like the side pod holders or nerf bars, spindle arms and the rear axle, those upset my OCD mind a little and I would address those. Whatever is chrome plated, rub it with some fine steel wool, maybe wetted with solvent, and the chrome can come back. You might keep it lightly oiled or clear coat it to keep the rust away. Won’t know the real condition of the kart chassis until you remove everything. I bet the underside is scratched up pretty awful.
Short version; just do a touch up on the bad parts. If you intend to repaint the whole thing, just treat (de-rust) the rusted areas and lightly sand the existing paint and paint over it. I often do a refurbish with as close to the original paint as possible, so if/when the new paint is chipped, it shows the same color underneath.