It is important, if I destroy your brain and grow a new one and start running the same program on the new brain your consciousness is still dead and its a new person living.
Computer AI models don't run on a single machine, they run in a distributed manner using different machines at different times. When you ask a follow up question thats not sent to the same machine, its another machine answering. So the consciousness one of those computing machines experience would be extremely fragmented and not at all conscious about any discussion with you, since it only saw a few fragments of it.
And no consciousness doesn't expand to cover larger distributed computations, otherwise social media would have developed a consciousness by now but it hasn't. Groups of humans don't start to share consciousness, it doesn't happen, so you can assume groups of distributed computers wont as well.
If I copy a text document from one computer to another, is that the same document or a different one? It's all just information. If you copy it, you have two, it's still the same until the documents start changing and go different directions.
> Computer AI models don't run on a single machine
It doesn't matter on how many machines it runs on. It's information processing, as long as it gives the same results, it doesn't matter how you accomplish it.
Consciousness isn't some magic thing that sits on top, it's the result of that information processing. You take random sensory data, the brain transforms that into "cats, dogs, you, me", it uses uses those percepts to execute actions, gets more data back and checks how the actions changed the world state.
Keeping track of what changes in the world were causes by actions of the brain vs things that happened due to other causes is the conscious experience.