Hi, Liztheartist,
The song may not be showing up because it is in the cloud, or because it is DRM (Digital Rights Management) protected, or because Apple Music was involved in the chain of purchase.
If in the cloud, download it to your iTunes library. If it is DRM protected you may need to subscribe to the iTunes Match subscription program to download a DRM free version. If the song was purchased from Apple Music at one point, it will be DRM protected even if downloaded to iTunes.
Just in case it may be a corrupt iMovie preference that is causing the issue, try deleting preferences. 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 your song appears in the audio sidebar.
-- Rich