Stone wall made of stone/stone slabs? Living room / kitchen

Such an adhesive would not be known to me at the moment.

Is it advisable to glue the Styrofoam boards onto the wallpaper? Then removing them afterward should be much easier since the boards are not glued directly to the wall. What do you think?

Since I’m currently at the hardware store more often, I took a look there. I saw panels that are not made of plastic or at least not recognizable as plastic, and these are apparently only attached with double-sided tape that is already on the panels. Maybe interesting for you? I would just go and see what’s available! Adhesion on wallpaper might be a problem if the load gets too heavy and the wallpaper then tears off. Whether that applies to your surface, I cannot say.

That would be too high a cost for me for a rental apartment.
Isn't there a possibility to discuss the matter with the landlord, then make it permanent (which might increase the living quality) and share the costs?
Regards

To be honest, as a landlord, I would not want to share in any costs incurred. My decision as a landlord would be, if a new tenant likes it, it can stay, if not, it must be removed. Therefore, do it in a way that it can be removed with little effort and still looks presentable.

Asking costs nothing.