You could put lining paper over the cork, so you have a paintable surface.
My flat has plaster render over brick for internal walls (external walls are lath & plaster).
My hallway has a styrofoam backed wallpaper. It gets damaged SO easily, and I haven’t found a decent way to repair it. I presume at some point, I just need to repaper it.
I think cork is a bit hardier than styrofoam, but just a heads up for high traffic areas
The cork I’ve been able to find specifically warns against painting it or covering it in any fashion. I could go for an accent wall on it but it is not a material easy to match and the texture is just off.
I may use cork liner on the floor before setting down wood pavement (I intend to reuse every piece of wood I can manage to salvage) but not on the walls.
And yes, styrofoam is horrendously fragile. At some point you may have to consider replacing parts of it, which apparently is very easy, but just putting up such a fragile material doesn’t make sense for me.