> but you will first catch a glimpse of heat death of the universe

That doesn't seem to be possible as information/light from the end of the universe would not be able to reach you.

There's a discussion of it here: https://physics.stackexchange.com/questions/82678/does-someo...

But is it? The event horizon will eventually be receding again, maybe enough to prevent you from actually falling in. However fast you're falling, you'll still need time to actually move forward. Time that time dilation doesn't give you.

Which of course is infinite, but not QUITE infinite infinite. The last light to reach you will be from the time the black hole ceases to exist, which is "close" (in relative terms) to the heat death of the universe, even if it's incredibly far away from it measured in years.

That diagram feels unstable. The region near event horizon is infinity valley, a small perturbation there can have arbitrarily large effect.