With iMovie 10 the way to access your iTunes songs is to open a project, click on the Audio tab at the top left of your screen, and then click on iTunes in the iMovie sidebar of the project. The available songs will be displayed in the browser. Try that procedure and see if you can access your song.
iTunes songs purchased after year 2009 should be free of DRM protection and are available for use in iMovie. Songs purchased before year 2009 would be DRM protected and not available.
Any song that was acquired from Apple Music, no matter what year, carries DRM protection and cannot be used in an iMovie project. Downloading it into your iTunes library will not remove that protection.
When you do a Get Info on the song either in the iTunes Media on your hard drive, or in your iTunes library by control-clicking on the song and then clicking on Song Info/File, it will show whether or not the song is protected. An unprotected song should be usable in iMovie. Since that does not appear to be the case in your situation, try dragging the song onto your desktop and from there drag it into iMovie.
If still no luck, try deleting preferences with the following procedure:
Open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects. Now see if you can access your song.
If still no luck, try repurchasing the song and see if that works.
-- Rich