End of time or a place without time are pretty much meaningless things for humans, because we require the passing of time. The end of time would be place of maximum entropy, a humanoid corpse isn't going to decay there, because it would have already decayed, and then all its constitutent atoms would have decayed, and then any constitutent protons and neutrons, and it likely would have fallen into a black hole by then (even if it takes gazillion of years). So if there are people there, it's not the end of time. And if we could somehow send people to a "time" where the time ends, the time would no longer end then and instead pass until the aforementiond has happened and nothing was left. But I suppose it could be that the place Who Remains stayed us would have been the end of time if he hadn't somehow time-travelled there, or something.
And the TVA might not be part of any other timelines and a pocket universe, but it clearly has a passing of time inside it. Maybe there are some cheats in it, that maybe it can violate the 2nd law of thermodynamics and basically resets to a lower entropy state or something?
In the end, this is really the fiction and not the science stuff. It does whatever the writers want it to do.
Though if I had to guess what the writers want it do:
Timely's Spaghettification is not his death, but actually a Time Slip, and he slips back in a past where he can teach Ouroborus about the TVA technology, with the handbook that OB has written and was given to him. It's a time loop.
And the catastrophe will be barely averted because Timely has already prepared something to fix the loom and it will activate at the last second or something. (Maybe still requiring some heroic efforts to actually work).