That's not a category error. GPT is general. It is able to perform many tasks (Creative Writing, playing Chess, Poker and other games, language translation, Code, robot piloting) etc
Arguments like yours are why I regard "generality" (certainly in the context of AGI) as a continuum rather than a boolean. AlphaZero is more general than AlphaGo Zero, as the former can do three games and the latter only one. All LLMs are much more general than those game playing models, even if they aren't so wildly superhuman on any specific skill, and `gpt-4-vision-preview` is more general than any 3.5 model as 4 can take image inputs while the 3.5's can't.
Yes. If you read "Computing Machinery and Intelligence" this idea of generality being a continuum is a point that Turing makes actually (albeit in different words). What constitutes generality of an AI is really going to be very sensitive to your metric and the assessment is going to vary a lot from observer to observer.
If we define "general" as tasks with text input and output we are severely restricting the domain.