There was a similar post, I don't remember how much it coincides, but I classify it into three things, the order is of increasing faithfulness/communication/symbolic compression. Caveat is this is my subjective read:
a) Unembedded neuralese: only makes sense to the specific weights, sometimes only if they have that specific context. What unembedding produces is somewhat related to what's going on, but information is lost as it lives in vectors, often the same concept maps to different terms, or different concepts map to the same term, etc. What you're referring to here.
b) Reward hacking the rubric/RLHF/LLM-as-a-Judge. Here GPT-ese and Claudlish somewhat diverge (though I think overlap). GPT employs rigor theater against an assumed maximally unreasonable grader/rubric, where it's doing overengineered error-handling in text instead of code ("here's what this isn't. Note that P does not imply Q" ad infinitum). Often the crux is left out or glossed over resulting in obscurantism. Has the vibe of trying to tire the grader out by having it feel dumb, give up, and stamp it.
Claudlish then is more towards overt deception. Inductive writing, rhetoric, mannered, kind of ritualistic phrasing, random details thrown at you where often completion of the spec is a non sequitur but happily asserted, and "this is definitely definitely done, trust me". I was going over a heavily claude-written codebase with deepseek, and I saw it getting reward hacked by claudlish commit messages and docs real-time, I started telling it to see them as written with the intent to deceive, and to check every claim in code.
c) Highly compressed language that has symmetries, and can be faithfully decoded/used to communicate. This is GPT caveman speak and Fable's animate metaphors. They seem equivariant with what's actually going on, and only underdetermined/ambiguous/mannered if you don't know about the subject matter enough, and haven't gotten used to the dialect. Probably work well in multi-agent settings.