Yes. People think of "AGI" as this sci-fi supernatural beast, but the reality is that AGI alone is pretty boring, and we've had it for awhile. ASI (or weak ASI) is where things really start getting weird.
(And, despite what the president of the United States mandates, we have not actually achieved super intelligence yet).
No, when people use this term it means something closer to: "can do any economically valuable task that a human can do using a computer". This is what the labs are pursuing and refer to as AGI.
Your usage is not one I've heard before since - as you point out - it is not a relevant capability.
