There's the philosophical argument that we have no continuity of consciousness in our meatbag bodies either - e.g. when you wake up, it's rebooting your consciousness from suspended memories.
There's physical continuity. You can be sure that most of your neurones will be the same tomorrow.
So to solve immortality, you gotta replace meat cells with silicone ones, slowly, one percent after another. It'll maintain relative continuity and hopefully will transfer memories and other person traits to the silicone, so one day the brain will be immortal and repairable.
But once they pay $$$ and turn on the uploaded consciousness won't they be like "Hey, why I'm still here in my meat body and not in Amazon Brain Cloud(c)"?
I thought the the fact that your mind is not magically booted into simulation while you are still alive (during sleep, backout while drunk or just pressing the power button on the server running it) should be a clue that you won't suddenly wake up in simulation after you have died.
Our language can't fully represent the possibility, as it doesn't currently exist and language is learned by mutually shared experiences upon which we then agree terminology.
If you make a backup of my mind every midnight, and at noon one day biological-me faces death, that's still death for noon-me, while also being a way to cheat death from the point of view of the me from 12 hours before.
Restoring your computer from a backup doesn't mean the hard drive never failed, but it is does get you data back.
No, our language is perfectly capable of expressing this simple fact: When you die you die, no matter how many clones or backups of you are up and running.
When you say "you", do you mean the continuity of consciousness (which is interrupted each sleep cycle), the personality and memories currently instantiated within your brain (which we don't actually know how to read yet never mind duplicate so the process of creating a backup at all is entirely hypothetical), or a soul?
When you say "die", do you mean clinical (cardiac) death, brain death, legal death, the cessation of internal cellular chemistry in more than n% of cells (which can itself take hours after legal death, but varies by tissue), or the irreversible destruction of the structures within your brain that keep the "you" previously defined existing at all (if you chose a non-soul based answer) or locked to the mundane plane (if you answered "soul")?
If any of your answers involves consciousness, Doerig et al[0] list 13 notable possibilities for what that word means, while Seth & Bayne[1] list 22.
Furthermore, consider the thought experiment of the ship of Theseus, and ask yourself: if you make a sufficiently perfect copy the ship, deliberately loose record of which is the original, destroy one of the two at random, can you see how our language does not allow us to say other than the ship has both been destroyed and survived?
You conscious thoughts might be asleep but some part of you is still "there" and operating or else you wouldn't be able to wake up and remember anything?
There would be no way to find out if that would be true however. The person in the vat might say they are the same person but you don't know if they really are. Also what happens if you create a copy? Is that two people or is there some kind of shared consciousness? If it is, how do they communicate?