OK. I just talked to Apple support. The behavior as described is by design. In short, there is NO WAY to play a single song and then stop. I'm a musician, and I want to play one song then stop - but that is impossible, currently. Here's what they say: With the Repeat1 icon highlighted it will play the same one song over and over again. With the Repeat icon highlighted, it will continue to play another song from the Playlist or Library, and when ALL have been played it will start over again. It will never ever stop. With the Repeat icon OFF (not highlighted), it will continue to play another song from the Playlist or Library, until that Playlist or Library has been exhausted at which point it will stop.
So now, this is my workaround to play a single song then stop: I create a playlist with only that one song in it, and disable the Repeat icon. What a pain.
If you want Apple to allow Music to play a single song then stop, please go to https://www.apple.com/feedback/apple-music.html and let them know. Here's what I said to them:
"Please modify the Repeat function to allow Music to stop playing at the end of the current song. Currently it is impossible to have Music play one song then stop. (It either repeats the one song or continues to play the entire playlist or library.) This is irritating to musicians like myself because we must stop what we are doing to stop the player when the song ends."