plk
Entry type for course
As far as I know, there is no proper way to reference a course in Biblatex.
Traditional (i.e. BibTeX) ways to handle this is to use to use @misc or @unpublished but those entry types are too broad.
The closest I could find in Biblatex is @booklet. It could be enough for some material of the course but I don't think it encompass the course as a whole (which may contain several booklets, slides, exercise sheets, web page(s), course notes, etc.).
Of course, a course is not a formal publication but I would say that it's rather close.
I have to confess that my goal is to use Biblatex to organise most of my documents and those include courses. So citation is not per se my goal.
You can always define a new entry type in a custom data model. See https://www.tug.org/TUGboat/tb35-3/tb111fischer.pdf or https://tex.stackexchange.com/q/175776/35864.
The usual biblatex policy is to add new entry types or field to the data model if they require new features (as a demonstration) or if there is high demand for such types/fields (ideally because prescriptive styles require them). See also the recent https://github.com/plk/biblatex/issues/1424 (or the less recent https://github.com/plk/biblatex/issues/969, https://github.com/plk/biblatex/issues/971, https://github.com/plk/biblatex/issues/880 and linked issues).
As you say the standard date model is well equipped to handle citations to course material, so biblatex's "core jobs" are well covered here. If you want to use biblatex for things that go beyond the usual citing and bibliography creation it is expected that you have to do some extra work.
Yes, I considered extending the data model but I saw opening this issue as a way to poke if there is interest in this type of entries (I mentioned my particular need for the sake of honesty). Maybe it's not the best way.
One context where citing such entries could be useful is when writing a CV or an application letter (in academia).