> would the concept of me and you as separate identities actually mean anything to us anymore?
Clearly yes. If your body is destroyed, I will stop experiencing your thoughts and your senses, and vice versa.
> You anyway go to sleep each night and awaken after a discontinuity. Why would this be significantly different?
I'm more interested in why it would be the same. As it stands, there is no account of what is the thing that persists through deep sleep, or more broadly, of why there is sentience to begin with. I'm perfectly ok with conjecturing that sentience is not physical, given that we can't observe it, like we can with the physical. And I don't expect we will find some physics redefining discovery in the brain that will allow us to see us. Some philosophers hold that the more interesting question is why do neuroscientific accounts of the brain seem insufficient to us, but at that point the jig's up, you're doing philosophy and not science. Which is the problem of mind uploading, there's no scientific surety to it, believing in it will be conditional on not thinking too much about it, or on taking the position that "the philosophy is settled!".
> Clearly yes. If your body is destroyed, I will stop experiencing your thoughts and your senses, and vice versa.
Well, assuming a copy of my mind was being perfectly executed by some machine, that would mean that even if my body is destroyed, along with the sensations and thoughts coming from the copy of my brain residing in my body, the machine copy will still continue to feel perceptions (through machine sensors or through your body) and think my thoughts. This would be roughly similar to losing a hand or an eye today - it is a loss, but it does not fundamentally affect your sense of you.
> As it stands, there is no account of what is the thing that persists through deep sleep, or more broadly, of why there is sentience to begin with.
Physics in general has no notion of anything persisting - as far as all our physics is concerned, there are just instants of time (and space) that influence each other (from past to future) but are otherwise separate. The same is true of course in space - there is no physical account for "an object". At the macroscopic level every "object" can be equivalently modeled by smaller pieces held together by various forces. At the quantum level, elementary particles are indivisible, but also indistinguishable: there is no distinction between saying "this electron moved from atom 1 to atom 2" and "the electron in atom 1 disappeared and a new electron appeared in atom 2".
Of course, this may mean that our account of nature is missing something much more basic than consciousness (persistence / the flow of time). Or, it may mean that identity is a fundamentally meaningless notion, an unnecessary (in the logical sense) heurisitc that evolution has bred into us because it is useful for predicting the behavior of the macro world.
Clearly yes. If your body is destroyed, I will stop experiencing your thoughts and your senses, and vice versa.
> You anyway go to sleep each night and awaken after a discontinuity. Why would this be significantly different?
I'm more interested in why it would be the same. As it stands, there is no account of what is the thing that persists through deep sleep, or more broadly, of why there is sentience to begin with. I'm perfectly ok with conjecturing that sentience is not physical, given that we can't observe it, like we can with the physical. And I don't expect we will find some physics redefining discovery in the brain that will allow us to see us. Some philosophers hold that the more interesting question is why do neuroscientific accounts of the brain seem insufficient to us, but at that point the jig's up, you're doing philosophy and not science. Which is the problem of mind uploading, there's no scientific surety to it, believing in it will be conditional on not thinking too much about it, or on taking the position that "the philosophy is settled!".