trying to download a purchased song for Imovie
I purchased a song to download/import to iMovie and I can't find it, and iMovie doesn't have it either
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You didn't describe where you purchased the song.
Apple Music songs are DRM protected and cannot be used in iMovie or other apps. It is a subscription service that streams songs for personal listening, if you continue to maintain the subscription. That system would be thwarted if one could, for example, download the song into an app and then cancel or let the subscription run out.
iTunes songs, as opposed to Apple Music, can be used in iMovie. The song would be found in your iTunes library.
---Rich