What if you add something to you that's knit into and augmenting your brain by 10%, and then as a little more of your brain withers, you add another chunk. Ultimately it reaches a point where your existing brain is doing none of the work and it's all machines, but there was arguably never a precipice crossed where it wasn't "you".
You may enjoy authors Greg Egan or Dennis E. Taylor.
Yah, well, mortal-me also eventually develops different motivations. There's still continuity and connectedness.
It's just fork(2).
Also some people might disagree with "digital copy of you != you". Personally, I do not care since it is close enough to immortality imho.
And consider: if I can upload, perhaps I can download. Perhaps my digital copy can live life 'faster'? In that case I live 1000 lives digitally and download that.
Now I'm essentially immortal, in my physical body, because I've lived for millennia!
At the very, very least its no worse than living this one life and dying anyway.
It would not be a dream any more than yesterday wasn't a dream.