How to apply 3D noise texture to mesh?

I’m having some trouble trying to add a simple 3D noise texture to an object generated by geometry nodes. I’d like this object to look like it’s ‘carved’ out of a rock like material, so I basically just want to use the local positions of the vertices to define sampling points within a 3D volume. However, I’m getting some weird artifacts and suspect that Blender is generating a 2D UV map instead. How would I fix this shader network so that my shape is being rendered with 3D noise?

The noise texture does not output normals, use a bump node to make (false) normals.

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