A planet to look at or a planet to walk on ?
And is your height map actually a cube map ?
I don't have a ready made cube-to-sphere algorithm, but there are several tutorials.
If you go the cube map way, the simplest way starting with a cube around the origin, let's say +/-0.5 on all axes. Then you stepwise subdivide each face of the cube, creating new vertices in the middle between each 2 vertices. Each vertex maps to a sphere simply by normalizing and multiplying with the radius.
I'm more of a low level programmer, maybe a colleague can tell how to do this in Godot. Start with a subdivided cube mesh instance and normalize/multiply each vertex ?