Closest Surface Point Driver

I’m looking for a way I could set up a driver that gives the position of the closest point on the surface of a mesh to a specified point. It has to be sensitive to animation of both the surface and point, as well as work reasonably for many points (so not hooks).

As far as I have been able to find, it’s only possible to use drivers to determine distance to object centers and (possibly, I couldn’t make it work) individual verts. Perhaps with some magic I could find the closest vert, but that is still not really what I want. There might be a significant difference between the closest vert and closest point on the faces.

What I’m trying may not be possible in Blender on its own, but perhaps there is an addon or script that could add such functionality?

with the attribute proximity node in geometry nodes you can extract the closest point in one mesh for every vertex of another mesh , but I am not sure whether this helps you in what you want to achieve in the end with your driver.