If we want to know if AI is conscious or not, we have to ask if the AI can recognize itself in the input it gets.
Some aspects like limited content length and lack of ability for the model weights to update will certainly limit what the AI can do. But that's ultimately a matter of degree, not kind, when it comes to consciousness.
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.