They wouldn't be us. We will still die when our bodies fail. But maybe there will be some AI tricking our friends and family into thinking we're still there.

You are making a claim that is theological, religious, and scientific. Yes, our form of life on earth ends when our bodies die today. But what is the essence of us, no one really knows. Various people claim it's locked into your body, or you have some kind of soul that depends on your body. Or your brain is just running a program and the information and mechanism dies when your body dies. I lean toward the last category, but no one knows.

The body is constantly changing. We already know about physical and chemical abnormalities in the way your body works affects your "person" and we can sometimes address them with surgery or drugs. The physical body's limits impact the observed brain. If uploading is possible, if there are some examples of working cases, if I don't hurt anyone why not try it?

If you have a stroke, and survive, you won't be you anymore.

Yeah by the same logic we die every night when we sleep.

What if it's an incremental upload? E.g. we start with some prosthetics and slowly migrate organic function to digital?

Is this the Ship of Theseus, or is it a slow but nonobvious death?

The Ship of Theseus is a weird one too. If you take a car apart and replace it piece by piece and replace the whole car you kind of have the same car. But what if you kept all the old pieces and put them back together? Which one is the original car? It is a interesting thought sub experiment that plays on the 'Ship of Theseus'. You could end up with the same issue here. If I make a perfect copy of myself, who is the 'real' me? There is an obvious 'older' me but the other one is just as capable as I am.

If you keep the original bioware fully operational, it's more like an incremental fork running on an emulator. You can start having conversations with your approximated self.

Immortal as long as someone's paying to run the instance.

You'll have tiered processing, just like today. You can slum it out with limited simulation capabilities, or if you have a job you can afford the premium processor hours.

See the Amazon Prime series "Upload" (two seasons so far).

Rather funny, BTW, compared to most works around a similar premise.

And then you'd have the first court case and prison sentence for a non-human consciousness.

Which is just one step closer to the simulated hell for uploaded consciousnesses that get naughty, from Surface Detail by Ian Banks.

The show upload on amazon prime is basically this world. If you don't have as much money your instance can pause. You pay more money and have access to nicer things in the afterlife.