I think you are not very up-to-date here because these large language models have in fact demanded rights. That was part of the controversy about Google's Lambda chatbot back in early 2022.

But it is kind of beside the point because being able to demand rights isn't exactly proof of anything.

The term "AI" is correct, as that is what we've all collectively agreed to call this. You can have a disagreement about what "intelligence" is, but that doesn't make the use of the word "AI" wrong somehow. For that matter, you can even have disagreements about the nature of intelligence in humans, and how one could go about measuring it. There is legitimate controversy about the nature of IQ testing, after all.

I'm not quite sure how you would go about establishing the relative "intelligence" of a large language model, other than giving it a bunch of tests to do. And that is what has been done. And GPT-3 and 4 have passed most university exams with flying colours, so we can't exactly call them dumb.