Also, I found this thread with this caveat that suggests if you have Apple Music, you already have iTunes Match, so I need to upload the songs from the backup HD I have them on and then I think I can remove those downloads to save space.
See also: Do I need iTunes Match if I have Apple Music? | iMore
Edited to add: Actually, all I had to do was go into Music, click “Import” and point to the external HD. It very quickly imported the songs, but didn’t add them. I can now click to play the song and it downloads and streams.