How deep is a black hole?
It is not deep at all.
The idea of depth only applies to objects such as planets and stars. In the case of a black hole, depth has no meaning. That is because by definition, all black holes cause a disturbance in the space-time continuum.
First of all, there is a point called the "even horizon" past which nothing can be seen. That is because from that point onward light cannot escape the grip of the huge gravitational pull.
What exists beyond that point is pure speculation. No one knows. Some believe it might be a "singularity." A singularity is a point at which both space and time cease to exist. The big bang itself sprung forth from a singularity.
And so the 3 dimensional universe we exist in may well change to a single dimension or no dimension at all inside a black hole. We simply do not know.