Well I haven't used BRT and I await replies with interest, but I'll just offer this -
as you've discovered, a 'Course' is a type of Track. As such, I would suggest Coursepoints are going to be Trackpoints and not Waypoints. That's why you can't see them on the E20.
Sorry that didn't help much!
[edit to add -
I think the E20/30 doesn't recognise 'Courses' as such - they are specific to the Edge-type Garmins and are distinguished by being TCX files (I think?) - however you may still be able to use a Course-oriented Planner provided it allows you to download the results in a way the GPS can use, ie a Route(s) or a Track(s) contained in a GPX file(s). Downloading as a Route or Track would probably convert your Coursepoints to named Waypoints.
The E20/30 'Where To?' menu is a bit too clever for its own good, it will only show 'Routes' and/or 'Tracks' if these are actually available. If they aren't available, you'd never know these options even exist. On that basis, I suppose it
could have an option for 'Courses' (because I've never loaded one, so I wouldn't know) - but somehow I doubt it.
Certainly, you want to be following one or the other, using 'Where To' to just go to a Waypoint is definitely the option of last resort.