OpenAI's own charter defines AGI as "Highly autonomous systems that outperform humans at most economically valuable work". This is actually fairly sensible and involves obviously a ton of non-cognitive, emotional, social and physical activity. In other words, if you can replace most or all human beings with a machine, you have something that's generally intelligent.
That's obviously not even remotely where we're at, AI chatbots do well on narrow usually text based or programmatic problems, but can't even replace a barista or a plumber.