Took it to my local source.

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.