> “it’s not x, it’s y”

ChatGPT does this just as much, maybe even more, across every model they've ever released to the public.

How did both Claude and GPT end up with such a similar stylistic quirk?

I'd add that Kimi does it sometimes, but much less frequently. (Kimi, in general, is a better writer with a more neutral voice.) I don't have enough experience with Gemini or Deepseek to say.