>AGI has a pretty precise definition, covering only cognitive tasks.

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.