I am not yet too deep into that, at least concerning the Godot part.
Question: What exactly means "planet" ? A real world celestial body or just a sphere with a limited diameter, like No Man's Sky or Kerbal Space Program ?
Getting the correct camera orientation is simple: usually, one would make the planet centre the origin of the coordinate system. One needs to control the camera up-vector so that it points away from the centre. On a sphere set at the centre of the coordinate system this is simply the negative of the normalized position. This is a rotation that can be done in a script, maybe you have to add a node that the camera is attached to (spatial?) to accomplish that.
Once that's done, new challenges are waiting: Movement on a sphere needs transformation between coordinate systems. And in case of precision problems solutions like relative-to-eye are needed. Not sure if you can replicate that in Godot (yet) with reasonable peformance.
But real world planets are not that simple, they aren't spheres and they are really big.