HomePod and Itunes library

When I initially set up my HomePod, using an iPhone X, not all my iTunes library was available. I reloaded the HomePod and now only one song appears to be available on the HomePod.

Both devices have the latest software and I use iTunes on my phone, NOT Apple Music or iTunes Match. I was led to believe that all my music (approx. 5000 songs) would be copied to the HomePod and I would not need to have my phone available in order to listen to my music on the HomePod. Am I missing something here?

I'v been unable to ascertain whether of not music is in fact copied to the HomePod or not. Can someone please advise me on this. If my understanding is wrong, why is one tune sitting there?