How to make a material(?) that highlights its edges at mesh intersections? Examples attached.

Worldcoords-XY is just way to tile a texture using worldcoords from top down. It would cause the noise pattern to stay constant in the world so if the sphere moves, you’d see different parts of the texture:

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Could just as easily use default UVs for the noise texture (by just not connecting anything or using a texturecoordinate node with any tiling). I was just giving options.

Using second depthfade with sharper gradient for the outer edge:
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Only have to do 1-x on the inner gradient.