Cloning is just making a new person with your DNA, it's not continuity of any of those

How does this apply to something like the game SOMA?

Body swap would be continuity of memory, but not identity or material.

I'd argue that identity and memory are the same thing. Like if you lose your memory, your identity becomes as strange as anyone else's. Or if you're a copy of someone else, you won't know it unless you were told and would think you're just that person when you wake up. Like if there was a transporter malfunction where it didn't destroy the original copy. You'd have one copy at the original site thinking the transport just didn't work and another one at the destination going about their life while Harry wonders how to tell Janeway.

What do you mean with "continuity of identity"?

PS: Sorry for the long text lol.

The only important thing for a human mind is subjective continuity of your mental process. Only the subjective perspective of the human mind matters to this question, and this subjective experience determines the morality of how we should treat others.

Material continuity is iffy. The cells of the human body continually renew themselves and take on new material, humans know this and do not care, as long as it is slow and not a complete break. But mental processes are irrevocably tied to physical material, and can't magically move from one to the other. So there can be no continuation of mental process without continuation of material. Both is the same.

Memory is constantly altered, forgotten, added to. It's crucial, but not an absolute since changes occur constantly. Humans know this and do not care much as long as they remember the important things, so this not that relevant.

People go to sleep or anesthesia or coma and the brain functions largely shut down, but the overall neuronal hardware stays like it is. People experience an interruption and continuation of their mental process as something perfectly fine. A pause in mental process does not end continuation.

The only thing one has to ask oneself is this:

If you could be copied perfectly and saw a clone appear next to you and knew they were a perfect copy with all your memory and thoughts, you would still not want to die. Even if that copy was improved, like younger or faster. We would not want to end our own subjective existence. We would still fear death. One only has to imagine seeing your own perfect copy and then being asked to put a gun to your own head and pull the trigger. Nobody sane who isn't suicidal would be fine with that, except in extreme situation. Like someone might volunteer for a suicide mission because it's important or vital or save many lives, but as a general rule it would be immoral to ask or expect people to do this. Or to normalize this, or to be dishonest about how it is experienced internally. There would always be outliers, but they are irrelevant to the general question.

So copying or mind uploading is theoretically impossible because it's unacceptable for the human mind in general. This will never change no matter the technology.

Some people might not realize what is happening and be fine with with being copied while the original dies (or freezes) at the same time, and since their personal experience of being clone number 100 feels like perfect continuation, they never figure out they die with each move (copy and delete). A self delusion. Human minds could also be altered to be fine with dying, but this would be such a fundamental and deep reaching change it would be very problematic and could be very dangerous too. It would be quite likely they are driven by pathological desires or fanaticism.

Merging two diverged minds might be possible, but this too would ultimately be fooling yourself. You might have two perfectly synchronized minds running in parallel on two different substrates, and both get the same inputs and thinks the same and neither knows which one is which, but neither would want to stop existing.

This would be a fundamental limitation and defining characteristic of human minds, and comes from having evolved from an animal. An artificial intelligence might not share these limitations at all and be much more powerful for it, constantly duplicating and deleting instances of itself without it feeling like dying.

There is still a theoretical sci-fi way to upgrade a human brain, to slowly upgrade one neuron and their synapses at a time over a long enough time span, like a year. The human mind would not notice or see any changes, only see the changes or improvements once it's done. That's really what the ship of Theseus tells us, if we change slowly, like humans naturally do, we do feel fine about it.

So instead of uploading we could slowly transform our brains into an upgraded substrate, transform into some kind of superior biology. Nobody would want to give up self-repair and that means biology, no matter what elements that biology would be based on. Features like complete introspection of all synaptic connections and activity would still be theoretically possible, even without being "digital". This could then be considered an objectively higher level of consciousness. You could review thought processes and emotional reactions. Also one could alter his own synaptic pathways and save revisions, but this would be brain surgery and physical alterations.

One could also add computing substrates to the human mind to improve your math skills and memory, run simulations or enter virtual worlds all within your own internal mind, or shared external worlds. Or move your upgraded brain to a new body or put yourself into tiny space probe. But without changing fundamentally what it means to be a human mind that evolved to fear death more than almost anything, you cannot upload or beam yourself somewhere else and expect either the original or copy to give up their life.

Presumably the brain of Thomas (if he has one) wasn't touched, so Thomas should be fine, as far as that goes. A horrifying existence lol, but organ transplants do not fundamentally change your identity.

if you lose to your memory, id argue that is losing your identity.

But none of them are continuity, only replication.