Is there any theory in the literature that supports this hypothesis that BHs in their center do not have a super-dense matter singularity but are pure deformations in the fabric of spacetime itself or vacuum space, possible caused after supernova or other violent event or maybe preexisted as features or defects of spacetime or vacuum space long before any matter creation in the Universe?
Is there any theory in the literature that supports this hypothesis that BHs in their center do not have a super dense matter singularity but are pure deformations in the fabric of spacetime itself or vacuum space
It's the General Theory of Relativity. The Schwarzschild solution for non-rotation, non-charged black holes is a vacuum solution, that is, the space is empty (vacuum): There's no matter and no radiation and no electric fields etc. anywhere.
The singularity itself is not a part of such spacetimes / solutions of Einstein's field equations. This means it is not correct and it makes no sense so say "there's a singularity of inifitit dense matter at the center of a BH", because the center is not a part of the space-time.
Your explanation in your comment:
My definition is the absence of spacetime or vacuum space inside the event horizon
will not work. If this were correct then the whole event horizon would be a single point in spacetime i.e. it would in effect have zero radius. In this case photons (which follow geodesics in spacetime) would be reflected from the event horizon, and to an outside observer the event horizon would show some distorted image of the black hole’s surroundings. But we know from the EHT images that the event horizon of a black hole is (as expected) black.