It depends on what you mean by the "inside" of a black hole. If you mean the event horizon, then for supermassive black holes, you wouldn't even notice that you

It depends on what you mean by the "inside" of a black hole. If you mean the event horizon, then for supermassive black holes, you wouldn't even notice that you'd passed it, so at that part of the inside, it looks exactly the same as outside. You might notice a difference if you tried to change your ship's direction and head "away", but you'd see that nothing you could do would let you get away. All geodesics point inwards. The insides of black holes are not infinitely curved, at least not most of the inside. That might be the singularity, but our understanding of that is definitely incomplete due to a lack of a theory of quantum gravity. And it does seem that nature abhors infinities, so the curvature of spacetime at the singularity is most likely not infinite, but we just don't know what it is.