purchased music won't play in iMovie

If it is Apple Music that you purchased, then it will not play in iMovie because Apple Music is DRM (Digital Rights Management) protected. Downloading it will not remove the DRM protection. Also, Apple Music is a subscription streaming service where you are only licensed, or renting so to speak, the songs to play for personal use. Thus, you cannot acquire ownership of the songs by downloading them to iTunes or to an app like iMovie.

However, you still can purchase songs from iTunes, as opposed to Apple Music, and those songs will play in iMovie.

-- Rich

If you are getting an HLS file, then it would not be an iTunes file. As I understand it, an HLS file is a streaming file, accessed from a website. Is it possible that Apple Music was in any way involved in the purchase process? Did you download it to iTunes from Apple Music? In your iTunes library, what format is shown when you control click on a song and then click on Song Info from the pop up display? It should be AAC or aiff. Does it show "Protected", in which case it is DRM protected and unusable.

The following link shows audio formats that are compatible with iMovie. HLS is not listed.

About incompatible media in iMovie for macOS – Apple Support (AU)

-- Rich

Hmmm. I don’t know what is happening there. You might want to call Apple Support and talk to the techs there. Click on the support button at the top of this forum’s screen and navigate to a place where you can input your telephone number. Hopefully they will have an answer.

— Rich