The Mac OS Music App does not show Playlists on a connected iPhone

Today I connected my (up-to-date with iOS 16.5.1 (c)) iPhone 14 Pro to my MacBook Pro (running 10.15.7) and noticed two things:

1) All of a sudden I did not have any playlists on my iPhone.

2) After restoring one playlist by dragging it from the MacOS Music app to the connected iPhone, Music did not not show playlist the playlist on the connected iPhone. I have restored several others and none of them are visible in Music (which is a step down from iTunes IMHO).

The songs are on the iPhone but the playlists are not.

Important: I do not subscribe to Apple music and wish I could disable it completely and make it invisible in the MacOS application.

I do not autofill directly from anything, I build playlists on the MacBook then drag/drop them onto the iPhone. I only very rarely do I purchase music from the iTunes store.

Questions:

1) How do I convince the MacOS Music application to show playlists when I connect my iPhone?

2) Where did my playlists go and why did they disappear?

Thanks.

NB: I have a recent iMazing backup but it does not back up music or playlists (although it does pretty much everything else).