Wallpapering behind the stove...

Photo wallpaper with the appearance of a rubble stone wall...

I don't know if you're doing yourself a favor with this in a new house: a photo wallpaper can create an interesting effect and enhance the room if you recognize it as such.
But a stone look can appear cheap.

Hm, you are probably right about that...

Then it will probably be the "real" stone backsplash after all.

Thanks for the answers!!!

I would clad with natural stone slips...

I would clad it with natural stone slips...

Me too

There are these slips at the hardware store, already finished in 10 cm x 60 cm, either with slate or with quartz stone.... both have something.
However, I would pay attention to the thickness of the slips, there are differences - I would avoid the > 4cm ones, the +-2 cm ones are better if it is just a small piece of wall

We have glued an entire wall with them within a residential unit.