I’ve been watching the TV series Pantheon and I really like it, but this tiny aspect is something I can’t quite grasp. So these people have their minds uploaded to the cloud - and they make a point to state that they’re still “them” - alive, real, authentic. But would it really be like that? The process is brain mapping, so essentially they just make a perfect clone of your brain/mind and run it digitally. But it’s still just a simulation. A perfect clone is still just a clone. The original person is gone. I don’t see the “continuity” aspect.
In the video game Wolfenstein, the side character Tekla goes on a wonderful rant about the continuity of consciousness.
https://youtube.com/watch?v=_4oU7sB_AJ0
If you want a darker aspect, the game SOMA is all about this concept, though it is meant as a horror game, so it explores all the worst outcomes.
Spoiler: if you have thought your share about mind digitalization, SOMA has a very predictable game plot. It’s a good game, but not as intriguing as, say, the Talos principle.