Purchased Songs from iTunes Store

There are multiple songs that I am not able to re-download or just download from the iTunes Store. When I click on "Purchased" in Music, it shows that I don't have any available downloads.

I have downloaded songs from the iTunes Store on my iPhone, yet they won't transfer when I try to sync my phone to my Mac.

I've chatted with Apple Support and they tell me that I need to subscribe to Apple Music?

Has anyone else running into this issue? Do I need to subscribe to Apple Music?