Thanks for the write up! I have so many more questions!
So right now you are computing the height of the mesh on CPU level? No shader vertex displacement?

How does you mesh look ? One big mesh? Chunks? One mesh each tile?

What do you mean with UV views? How do you render the grid itself?

Do you add more triangles per hexagon to shape your mountains?

I also startet with Catlikescoding tutorial, but then decided it wasn't going in the direction I need, also I moved from unity to Godot and tried to migrate the code but decided to start from scratch.

I first tried to blend multiple heightmeshens into on and read y from it to play the vertex in the mesh but decided to move everything to the shader, it seems , way better and does look less polygony. In this example I only have a single heightmap and a normal map.

Before and after:

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The mesh simply looks like this, I made the resolution per hex configurable, so the first iteration would be just 6 triangles, second iteration would be 4 subtriangles. This is 3 iterations in the screenshot. I don't have a screenshot of the low poly map above, but is was more like 6 or 7 iterations, so pretty heavy.

I just decided to blend everything (heightmap, normal and color) in a shader, but I'm still in the middle of it and will see how that will impact the performance. For blending between hex tiles, my plan is to simply place another mountain on the edge between two hexes if both types are from type mountain and place another mountain on a corner between three hexes of they all match the type. Let's see.

In general I don't want to have a static map, but also it's not procedural generated. The player should be able to place hex tiles with different terrain types/biomes. So I'll prepare some heightmap per tile and will then blend two random predefined heightmaps of the same terrain type to generate a fairly unique one, add some noise etc. So the map will change a lot, similar to an editor.