Suppose you died every night in your sleep and were replaced in the morning with a perfect copy of yourself with all your memories intact. Would you know the difference?
There would be thousands of copies that experienced going to bed and then nothing afterwards.
I only really managed to assuage my fear by realizing there would be an incredible number of dead bodies to deal with if this were happening to everyone every night, and it was extremely unlikely it was only happening to me.
So you have no need to fear the inevitability of death, only fear the inevitability of the desire for death.
Finally, to cure the fear the inevitability of the desire for death, live your life so well that even if you die accidentally, it's worth it.
Same for other contrived things like dying and getting revived every day, getting frozen and unfrozen every day, taking a teleport dematerializer every day for your commute, having a portion of your brain and organs randomly get swapped out ship of Theseus style, etc.
At some point you would just come to terms with the fact that your existence is really just that of being a mind with a past and present. The future doesn’t really matter.
My point is that I suspect most of us wouldn't do anything differently, even if we know it's not our consciousness continuing on, because both scenarios are identical for all practical purposes.
First, how did I find out about it? If someone else discovered it and proved it and then told me, but they have not yet published or told anyone else I'd seriously consider immediately killing them (or waiting until they fall asleep and then killing them).
Widespread knowledge that everyone dies every day and is replaced by a perfect copy would be devastating for the world.
Assuming that I'm the only one who knows this (either because I discovered and proved it somehow, or because I just killed everyone else who knows), then I'd probably treat it the same as I would treat finding that I have an incurable illness that is going to painlessly kill me that night. I then have two options:
• Let that happen.
• Die by some other means before then.
In favor of the first option, letting it happen, is that the next day the world has a perfect copy of me that, assuming that most other people do not know that everyone dies and is replaced nightly, the rest of the world believes is me and that behaves identically to how I would have behaved had I survived to that day.
But I have no one that actually depends on me. The world does not actually need me to still be here tomorrow. Some friends would be sad if I were gone, but eventually the line of copies of me is going to end when one of them dies other than by going to sleep, so my friend's copies are eventually going to be saddened by the end of the line of tzs copies anyway.
That brings us to the second option. There are people whose lines of copies are bad for the world. So why not get some guns and take a few of them out? That has a good chance of getting me killed but since I'm dying anyway that night, so what?
There's the moral issue of taking another life, but the people I'd be killing are also going to die anyway that night. I would be preventing a line of copies of them from coming into existence, but preventing something from coming into existence is usually not seen as equivalent to killing something--the widespread acceptance of birth control is evidence of that.
As a practical matter, there would probably not be time enough to actually do this before falling asleep--but my copy tomorrow would know all this too, as would the next copy the day after tomorrow and so on, so could continue with the plan.
It is possible that I (or one of my future copies) would decided that killing is sufficiently wrong that even killing a very bad person who is going to die anyway in a few hours to prevent future bad acts of their future copies is not acceptable.
In that case I'd still consider the second option, but instead of death by going vigilante on evil people I'd probably just start doing things that I've always thought might be fun but had too high a risk of death to consider.
Not quite the same scenario, but the short story "All the Myriad Ways" by Larry Niven covers a kind of similar situation. In that story people develop travel to parallel universes, and discover that the idea that every possible decision creates parallel universes where that decision went different ways is true. The story is about the social implications of that as many people decide that nothing they do actually matters.
If you had the choice of pushing a button that would kill a total stranger that you never met, would you do it? If not, you can use the same argument for your friends. Sure they may be replaced by identical copies, but they will still experience feelings, although they are technically not your old friends
Subjective continuity is illusionary, you placing import on this illusion is up to you of course, but there is no substantive difference between the discontinuity experienced by your 'copy' in the cloud and what you experience yourself moment to moment.
Invincible also tackled this problem, with someone cloning a new body, and copying his brain to a new body. For a brief moment both bodies perceive the same thing before their experiences split into the two bodies. The copy wakes up, says goodbye to the original, who is dying, and says "I'm sorry it wasn't you."
This is also IMO related to the ship of theseus problem. Are you the same person you were 20 years ago? Are you the same person in the morning as the person who went to sleep? Are you the same person as a minute ago? What if you add in concussions/memory loss/degenerative disease?
https://memory-alpha.fandom.com/wiki/Thomas_Riker
This is a similar vein about time machines