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The singularity in a non-rotating, non-charged black hole is as you say. It’s like in a finite amount of time you “run out of time”, like there isn’t any more time on that trajectory.

The singularity in a rotating black hole is entirely different but the interior of classical Kerr (rotating) black holes is one of the most controversial if inconsequential topics in theoretical physics because there are reasons to believe (without real proof mind you) the Kerr solution is unstable inside the inner event horizon so that whatever happens in there is not what that theory says.

And of course black holes are quantum objects which might actually have an “interior” entirely different from the classical picture.

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To be honest I really can't get past what "the end of time" even means.
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If it signifies the end of time, then all the stuff in the black hole would need to no longer exist no? If anything is happening in the black hole, then time is still progressing, so nothing must be all that exists?
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The more interesting component is that black hole physics is almost an anti-free will zone.

Everywhere else in the universe with mass and energy you can do what you want (sort of). An event horizon throws a hard shroud over that and drastically reduces opportunities: your free will to use mass and energy is significantly curtailed (you must head towards the singularity).

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I’m not sure free will has anything to do with it.

If you don’t have enough upward velocity to escape earths gravity, hitting the ground is also inevitable.

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