Thanks, that's helpful. I assumed Crisis on Infinite Earths had just referenced non-Arrowverse shows and films - I didn't know any references went the other way.It does. However, that doesn't make it Arrowverse any more than the DCEU or Stargirl.
The Arrowverse, I would say, used to refer to the entire multiverse. Then, when Crisis on Infinite Earths happened, that could no longer be considered the case due to how many things were connected.
So, Earth-Prime is the Arrowverse for simplicity. Earth-1, Earth-38 and Earth-BL can be taken as Arrowverse due to Earth-Prime being a merger of those worlds.