Can I paint over 90's style wall paneling?

Is that a paneling tile? Sure you can paint over paneling. If you can paint over linoleum tile, and paint over ceramic tile, you sure can paint over a paneling tile. Here is a Hometalk page where people have painted linoleum floors as well as ceramic tile.

https://www.hometalk.com/search/posts?filter=paint%20linoleum%20tile

I am sure depending on the material of that panel you will find the right project that would correspond with this. Also, if it is a smooth shiny surface which I can't tell from the picture, you will have to sand it first to get any sort of primer to stick to it. Good luck! Looks like a fun project.

It appears that it is tile board which can be painted but you will need to use something like Homax or RustOleum tile painting kit.

Yes indeed my friend painted hers you, first you need to paint it with a good bonding primer then I'd suggest a paint for especially made for high humidity areas like your bathroom. Here's the one I used for laminate it worked excellent, there's another one called Stix which works the same.

Tile board. A porcelain finish over hardboard. Yep it can be painted just like painting regular tile. Rustoleum or Homax tub and tile paint kits.

Yes, I did it myself

Wash the paneling, Sand if there is a film or shine, wipe and allow to dry. Then, Use a really good prime like Zinsser and paint.

Yes, start with a clean surface and then prime and paint.