I suspect there are new invariants emerging. We don’t know what they are and we will probably have to reach into the liberal arts to describe them but to me what you’re seeing is akin to the subatomic world exposing itself through diffraction patterns.

You're just looking for the study of rhetoric. LLMs have clustered on certain rhetorical patterns/gestures, probably because of a combination of frequency in input and bias in training. But rhetoric also concerns the logical structures that underpin communicative techniques, and it's this logical infrastructure that's shaky or bizarre in LLM content (like the GP noticing how "pushback" always resolves without further examination).