Why are existing entity reference fields not available to add to a media type?
I found the resources I was looking for with help from a comment by Clive:

A field can only be used on the same entity type. There is an open issue for this in the queue. According to the issue and my recollection this is a change from Drupal 7. If so it feels like a major regression.

The documentation is also incorrect at the time of this writing.