This is what I have done lately:
I have a no-name hot knife I got years ago that works well, and some of the foam factory tools as well as some wood burning stuff. (Solder iron with and exacto blade tip, good for fine lines)
On coatings
I know some people have used the smooth-on 3D coat material for foam with good results 9it should not eat into the foam.
I found that wood glue works surprisingly well.
I have tried various plaster products. But they don’t stick well to the foam and can chip off over time.
I have not done resin hard coating because of the expense. (From what I researched years ago, most large foam props were coated with a 2 part spay on epoxy using large spray equipment. But it was expensive and they would call someone out to shoot all the stuff at once. Then detail paint over it.)