In case this applies to you: If Apple Music was in any way involved in the purchase of the songs, then they wouldn't show up in the audio pane in iMovie. Apple Music songs are DRM protected, and the protection is not removed by downloading the songs to iTunes.
if the above is not your situation, you might try deleting preferences and see if that cures it: To delete preferences open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie usually will open in a new empty library. If so, reopen your old library to get back to your projects. Possibly you may need to reboot to set the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
As a workaround, you can open your iTunes library from the iTunes app side by side with an iMovie project, and drag the song into iMovie. Possibly you might need to first drag the song to your desktop and from there drag it into iMovie.
-- Rich