Is there no way to re-download purchased music??

I bought an album in 2017 from apple music/itunes. I deleted it at one point, but now decided I want it back in my music collection. I can't re-buy it, as the link in the apple music store just shows "purchased." I contacted support and they had no idea. They couldn't send me a download link despite it appearing in my purchase history and having an order number. They said someone would have to call me and then do screen share or something. I'm not sure why this is so complicated. It's not an unusual or complex issue. I guess I'll just have to re-buy the album somewhere else and then put it into my collection?