I agree with your sentiment, but I’ll say I’m in my 30s and in grade school they definitely taught us mean/median/mode as being ways to measure the average. That said, I do also use average to mean mean as that’s what something like Excel calls it and that’s what most people think of when measuring average unless you specify otherwise. So that’s all to say, yeah it’s a bit messed up.
Communicating more effectively with the world requires you to meet the world where it’s at.