I have almost always had issues downloading songs, at least on my iPhones. Idk if this is also your situation, but I have a HUGE music library and aside from my iPhone 12 pro, I use iTunes on a PC to manage my library. I found that I had a better chance of my songs having less issues on the phone if I would also go on iTunes and resync my library, especially if I hadn’t done it in a while. I also made a smart playlist that listed all of the tracks that had errors (low and behold all of them happened to be the songs I couldn’t download on Apple Music) and I tried resyncing them. For the ones that didn’t fix, I attempted to play them which sometimes would also fix the issue. Another error I found was with duplicates. Once I removed the duplicates, the songs synced. Once I had all that in order, and I force-restarted Apple Music on my iPhone, the songs downloaded. It was a huge headache, but so far everything now works. If none of this works, you can also try deleting the song (sometimes Apple Music will say it’s downloading but then act like it already finished by giving you an option to delete when you long press). If all else, you can also go to the settings and turn off “sync Library” and then turn it back on, but that’s a little more of an extreme option.
Hope some of this helps!