Apple Music songs are DRM (copyright) protected and thus cannot be used in iMovie. Downloading them into iTunes will not remove the DRM protection. Also, Apple Music is a subscription service intended for streaming and listening to songs, and not for using them in projects. As you have found, they won't work in projects.
I believe that you can still purchase songs from iTunes, however. Recently purchased iTunes songs are free of DRM protection and so they can be used in iMovie. Songs presently in your iTunes library are still available as well for use in iMovie if they are not DRM protected.
-- Rich