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.
I get what you mean, but to follow on what @woodscientist said, I think your persistent ego is essentially a subjective impression you have.
Your sense that the “you” of today is a direct continuation of the you of yesterday is a feeling you have. If someone simulated your mind, that construction world presumably wake up convinced that it was a continuation of your ego just as you do every day. If you were still around, you’d probably insist that you were authentic and it was false. That assertion is intuitive, but ultimately neither of you can be proven correct. Both interpretations are subjective and equally valid.