So couple of things. Physicists say if our current universe is infinite, then there are identical you's out there right now. Do you sense them? Feel their anxiety? No. So while they may be identical to you even living the same exact life as you (when things get infinite, the probabilities of this happening become very likely, infinity is big, really big). We don't know with certainly our whole universe, including the vast part we cannot every communicate with or observe, is in fact infinite, but it could be. Then this scenario likely is true probabilistically.

But you are missing something with the big bounce, it would be a mistake to assume in the next bounce that it produces a universe like ours, with our physical laws, atoms etc. It is quite possible maybe even likely that most, and am talking a very high percentage are universes with different physical laws where you literally could not exist. Change the physical laws, you get a different universe, it could be a universe that contains no atoms at all and may have something else. If conditions for life are possible there, that life would be very different, most of the them would probably not have the needed conditions. A lot of thought has been put into our universe's laws and we find them balanced in just the right way that conditions developed where life could even exist. Some physicists say our current universe may not be at is ground energy state, put simply it could be at a temporary stable state that hypothetically could drop into a lower, more stable energy state. If that would happen, our universe would be "consumed" by this new state and in the process will wipe out the current universe and all that we know would change into a universe with different key physical properties where we could not exist after being wiped out from existence. Don't worry about this because if it does happen we will not be able to see it coming at us as it would move at the speed of light, and once here on earth you would simply blink out of existence without having even a moment to think about what is happening.

We do not have the ability to tell what our universe was like at time zero, that is a singularity where our current physical laws break down and we do not have any idea for what exactly existed at time zero, we can only see so far back in time to the big bang, which is not time zero when the singularity existed. The big bang, as far as we can tell wiped out any evidence that could be detected before it happened.

So the big crunch would return the universe to that singularity. In that singularity we have no information on what the physical laws existed, as our physical laws were spawned out of the big bang. We do not have a current theory of quantum gravity that might give us some insights but we can never know time zero. So with infinite bounces, probabilities (again infinite is big, really big) some of those bounces, a very very very small fraction of which would like make another universe with the same physical laws as our current one, where as the vast vast majority of the other universes quite likely have different physical laws that precludes life of any kind forming. Another might have physical laws that allow life, but this does not mean it would be life like ours. That universe many not have atoms and all the other stuff, and have something completely different. However, infinite bounces is so many bounces that probability wise we could not only end up with a universe with physical laws exactly like this one, but infinity universes would also mean there would not only be universes like ours, but also some that play out exactly like this one right here, including making a new you, exactly as you are now, having lived the exact same life as you are now identically. However the future universe "you" will have no connection to you now in any way, even if that other you lives an identical existence. That other you may experience everything there is about your life, feelings etc., but has not connection to you now. It is a copy of you, not the actual current you, and our current understanding of how this might play out would mean anything about you, evidence you existed, your entire existence will be wiped in that crunch back into a singularity. So you would have ceased to exist, and latter a copy arose identical to you, but with its own conscious existance and no knowledge of you now, or of any of the other infinite you's that have been, or will be. Infinity is hard to mentally conceptualize, our brains cannot comprehend it beyond mathematical descriptions. So many other universes different than our own would form, but infinity being what it is, there would be infinite universes that form and develop exactly like this one with you doing the same things again in life in that universe, but also other universe where you are different and live a different life than you have led here.

The heat death may be a different situation. In that scenario the universe expands and keeps on expanding till the universe is dark, energetically homogenious without enough energy to perform any "work" in the physical sense, maximum entropy, empty, cold, not atoms as they have been torn apart by then and cold. That could be the extent of it, and it just stays that way forevere and ever. No planets, no stars, no black holes, just a very low level of energy that is too low to do any work, so it stays that way. There are some hypothesis that the heat death could allow certain quantum effects to occur that would spawn a new big bang out of that dead universe. But practically speaking we don't know if that is what would happen, or it just stays cold, dark and dead for enternity. This is assuming time still exists in the heat death scenario. One of the theories of what "time" is that it is a function of increasing entropy in the universe. If this is true (we don't know if this is what creates what we experience as time), in the heat death, entropy has reached its greatest disorder possible (more or less) and if so, does time continue to exist? Depends if the entropy changes are in fact why we experience "time" (note there are other theories). And that could be it, and it simply stays that way. A lot of what I described here is mostly hypothesis, and like a big crunch, we do not know if things will play out like this with any certainty. Just hypothesized possible ends that we can never be sure will happen. We won't be around to observe it as we would be long gone.

So don't worry, any future you's will live their own identical lives, but the current you would not have any connection with it in any way whatsoever.