This is a pity and a great limitation. I am in the same boat. I use an iPod in my car, and I thought I would be able to listen to new music which I have added for offline use from Apple Music.
The interface/effect of viewing and choosing new music seems different in itunes when compared to how it works and tracks added on my iphone.
So - to listen to new music in car I will need to plug in my iphone, in place of the ipod, which is inconvenient.
I might not keep the subscription. Spotify may have aspects which are better . . .
I can see the replies above about iPod nano not being connected, not running iOS, but when I read the Music blurb I felt that obtaining a track for "offline" use would include listening on itunes and ipod.
In the UK, Music sub may not be worth the money. I might still be better buying music and then sort of owning it. If you have ten years with Apple Music and you stop the sub, that music will all disappear.
Tony