> it feels weird to call values of type (Maybe a) functors as well.

Yes, that is bogus. If you're tolerant of math jargon, I found this article demystified the topic more than anything else did:

https://en.wikibooks.org/wiki/Haskell/Category_theory

And this explains where the monad laws come from:

https://www.haskellforall.com/2012/08/the-category-design-pa...