I don't know what you mean by restricted as singularities.
They are singularities.
Mostly that means that you can not know what is in the singularity region. The only thing you can know is effects outside the singularity region.
All known black holes are large massive objects.
Quantum rules like wavefunction just don't apply.
Heisenberg's uncertainty principle says you can know momentum or spatial location. Not both.
Hawking's quantum black holes have never been observed. I've seen some speculation that electrons are quantum black holes. If there is any meaning to this at all then reality would be quite distinct from Hawking's ideas.