That said, trying to distill what is being said here, the concrete action is [stop telling the AIs] that [they are conscious or on a path to consciousness]. Is that accurate?
The major premise seems to be that [they are conscious or on a path to consciousness] is an untrue statement. That's the essence of the sections "Circular reasoning" and "Anthropomorphization" and "Consciousness is very likely biological" and "AIs are simulation machines".
The minor premise seems to be that [consciousness is the basis of human rights]. This is the point of "Human consciousness is the cornerstone of our legal and ethical rights frameworks"
And the conclusion of the syllogism is that this is dangerous, that "Anthropomorphization amplifies AI safety risks". Specifically "seeding doubt about the moral status of AI systems into their own training may significantly elevate the alignment and containment risks of those systems."
I find all the arguments in the major premise section to be poor arguments but I accept the conclusion for sure that they are not conscious, and I can provisionally accept the idea that they are not on a path to consciousness.
I completely reject the notion that consciousness is the basis of human rights. The premise itself is absurd. We only have one unambiguous example of a class of conscious entities, and that it humans. If a human loses consciousness do they lose rights? If an entity gains consciousness does it get human rights? The former is a clear "no" and the latter is a "insufficient data for a meaningful answer".