Pressure Increase in stone and in water
Why does the pressure increase only by 0,3-0,4bar per km in stone but 1bar per 10m in water while stone has the higher density?


Because it doesn't!

Plots in this Physics SE answer and here and here show about 0.4 or 0.5 $\times 10^6$ bar at 1000 km depth, which is 0.4 or 0.5 bar per meter compared to your 0.1 bar per meter for water. If rock is 4 to 5 times denser than water, then all is well.