I assure you my young adult kids and their friends mean uniquely ChatGPT in the AI context. And whenever used as a proper noun, or as a person (e.g. Chat told me…) it means ChatGPT.
They also use it generically as the regular noun ‘chat’ when they’re talking about chat rooms and livestream live comments, (eg. “Paste in chat”)
My California highschool senior agrees that “chat are we cooked” is a reference to generic chatroom / livestream comments. To my surprise it’s a thing you can say out loud in a group to signal a local broadcast, ie. “hey everyone, are we cooked?”. I quite like that idiom.
On the other hand, they are very clear that the word ‘chat’ with no other context, defaults to an AI chat bot, assumed to be ChatGPT.
I withdraw my claim that this is common or universal. It’s frequent in my house.