You keep quoting research ad-verbum as if it's gospel
No, but I have learned over the years that when you see multiple papers discovering similar things at odds with the held consensus and see some even independently replicated that there's usually more than just smoke.
If this article was entitled "Researchers find patterns in neural networks that might help make more effective ones" no one would have a problem with it, but also it would not be newsworthy.
The paper was titled "Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models." Quanta, while a Pulizer winner in 2022 for explanatory reporting, is after all a publisher not a research institution. Though I dispute your issues with the headline as it's in line with similar article headlines such as "Bees understand the concept of zero".
I posit that Category Theory... Do you have an opinion on that?
You wouldn't be the only person looking at it through that lens. It was more popular a few years ago I think, and hasn't really caught on for LLMs vs other ML approaches and here it strikes me a bit like those with hammers looking for nails - the degree to which there's functional overlaps in network introspection such as the linked Anthropic work suggests to me that the internalized delineations are a bit fuzzier than would cleanly map onto a category theory view - but it's possible that as time goes on that it gets some research wins assuming it can come up with testable predictions that are successful. But it's more of a 'how' than a 'what' question - whether a network understands abstract concepts tangental to language it is trained on and develops world models (an idea that would have been laughed out of the room just three years ago by any serious researchers despite your impression) using something that can be explained through category theory or through another interpretation, the result is arguably the more important finding than the interpretation of the means.
It seems like you may be more committed to arguing the semantics and nuances of the tree in front of you than discussing the forest - that's fine, it's just not that interesting to me in turn.