Imagine ChatGPT 5 or 6, where it's at the point that it's entirely indistinguishable from a human, by any one of us. At this point AI can mimmic every aspect of being a human: emotions, reasoning, intelligence, memory.
Will you, at that point - which isn't far away - still claim that because it's based on matrix multiplication it can't possibly be doing any of those things and none of the behaviours fooling everyone are actually there?
How something is built does not limit its abilities. Only what something can do limits its abilities.
AI has certain abilities now.
Whether they emerged, were built-in by careful design, or don't even exist and just "seem" to, ultimately isn't even relevant to the most important fact of the matter, which is simply that it has those abilities.
To answer your question more directly, the emergent behaviours I'm seeing are: all of them.
That is, anything it seems to be able to do well enough to be useful and reliable, has emerged.