I watch a ton of your videos, thanks for making them. I just realized something. Perhaps this is answered in the links you posted, which I will study this weekend.
I see that the note of E is in the C major scale. But, the E major chord contains the G# as its 3rd.
As you note, G# is not a note in the C major scale. So, does this mean that the E major chord is not in the key of C major also?
I always assumed that because the E note was in the C major scale that also meant that the E major chord was in the key of C as well.