Where's the singularity that occurs if we assume it's just a region of space with nothing in it? I didn't call the black hole a zero-dimensional point.
We don’t know, and may have no way of knowing. There are conjectures that the event horizon is it, that inside the event horizon is a quantum fuzz ball, or strings, or 1D points, or a whole universe. We don’t know, and may well never know. What we do know is that it seems a 2D horizon can encode the information required to describe a 3D volume, and that goes for event horizons, as well certain classes of cosmic horizons in some models. This weirdness is the core of the holographic principle conjecture.