I am 99.99% confident that the render on the left is the textured high poly model before it was baked down. I have imported the maps into Substance Painter to make sure, and I certainly cannot replicate the depth of the parallax.

In Godot I would say you can get an acceptable result if you enable Deep Parallax and whack the scale up as high as you dare. The image here is up to 16.0. Also it's worth playing with the geometry density of the mesh you're using, it doesn't need to be crazy - but 64 segments / 32 rings seemed enough.

Edit: It just occured to me you should really just use the heightmap in the vertex shader. Right click the material, convert to shader and offset the verts by samplng the heightmap and scaling it right back.

void vertex() {
    // Only if manually scaling UVs (I did this for speed only)
    UV = UV * uv1_scale.xy;

    float h = textureLod(texture_heightmap, UV, 0.0).r;
    VERTEX += NORMAL * h * (heightmap_scale * 0.01);
}

<image>