As I understand it, any question about the interior of black holes is a question about the future. (And a very special subset of possible futures - see below).
The concept of a universal "now" was dropped with relativity (although frequently people ignore this). What we are left with are the concepts of regions of space-time between which signals can pass in one direction or the other. In addition there are regions between which communication can pass in neither direction.
There is no point on or inside the event horizon of a black hole which can communicate with a point outside this region.
In fact, if I understand the classical view correctly, the region nearer the singularity cannot communicate with an observer falling into the black hole even after it has passed the event horizon (the radius is timelike).
The singularity is thus of relevance to the future of anything that falls into it, concerning precisely what happens when it reaches the region very close to it.
I also understand that all this is compatible with the view that (to outsiders) black holes appear to form and evaporate through Hawking radiation, because this process is indistinguishable from a view where material accumulates just outside the event horizon, becomes practically invisible as it gets very close and the entire energy is radiated from very close to the event horizon. The story looks very different to the observer outside and the one who falls in, but since the one who falls in reaches the singularity, they are not going to compare notes.
I am sure there are subtleties which explain this picture better; if there are inaccuracies, perhaps someone better informed than I am can correct them.
This (classical + Hawking) picture described appears to be very different to the
fuzzball picture. In the former, when an observer crosses the event horizon, nothing very special happens; in the latter I read that the observer enters a region of high density, regardless of what material has recently been falling in (presumably). This needs clarification.