can not sync my music library to my iphone

My Mac has Sonoma 14.6.1 and my iPhone 15 Pro Max 1 TB iOS 17.5.1

On my Mac under Music Older Libraries and Media Music Media I have a large library of non purchased music. When I try to synchronise my library with my iPhone 15 with either option 1 Entire Music Library or option 2 Selected albums (then with all Artists tagged in blue - ?) nothing happens at all. Only videos are synced. No Music. Even when iPhone back up is changed from iCloud to the Mac itself.

I believe the above is due to Apple forcing all its clients to subscribe to Apple Music.

Please help me as I really am getting desperate and frustrated by this too long problem now.

I have some knowledge where the concerned music files are stored on my Mac. Thanks for your help !