Singularity is infinity
it's just a fancy word for "Our theory can't explain this thing" but they don't say it clearly (likely for funding purposes)
it's insane to try explaining the singularity with the theory that causes it
Someone need to find a better theory and Noble Prize is waiting for him

anb BTW, according to Schwarzschild metric there are two singularities in a black hole
the known one is when the radial coordinate = 0 and that's at the center of the black hole
the unknown one is when the radial coordinate = Schwarzschild radius and that's the even horizon
You rarely hear someone talk about the second singularity because it has it's fancy name

I didn't said singularity or infinity exist
I meant the exact opposite
General Relativity ends at the even horizon

someone needs to come up with a new theory that doesn't cause an infinity at the even horizon not trying to explain the infinity with the theory that causes it