Can I paint wet room flooring?

Sure. Clean the floor meticulously. Hand paint with Kilz or Rustoleum water-resistant primer and paint in one. Give two coats, drying between coats. Seal with oil-based polyurethane, 1-3 coats, letting dry a day between coats. Let it cure 315 days before it’s walked on. That’s five or more days from beginning to end. Then the floor should last more than two years if it dried and cured enough. ☺️

Personally I would not paint it. I've already experienced years of problems due to my driveway having been painted by the former owner. I would first use some "standard" cleaning agents with a stiff bristled brush. Then if it doesn't work, move on to stronger agents.

https://www.altro.co.uk/Support/Cleaning

https://www.google.com/search?newwindow=1&rlz=1C1SQJL_enUS800US800&q=cleaning+wet+room+floor+tiles&sa=X&ved=0ahUKEwiZ5-ui6MvbAhUOSq0KHb5iB0YQ1QIIigIoBA&biw=1280&bih=891

Rustoleum sells a tub refinishing kit. I imagine this would hold up on a wet floor as well!

I painted bath floor with kilz indoor heavy duty stain blocker ( pressed wood) new toilets new wax ring. In front of toilet semi circle looks like water came through the kilz