Synching Music, Mac to iPhone12

I am experiencing problems when synching my music library to my iPhone 12 mini. I have tried synching a number of times - even to switching off the Synch and logging out to erase everything and re-loading. but it doesn't all synch across. My library is a mix of my entire CD collection and, in more recent times, albums purchased from Apple Music iTunes.

It is a reasonably extensive collection - is there any way I can get everything from the Library on my Mac to my iPhone? I use Apple Car Play in my vehicles - hence the frustration when I discover the album I fancy listening to is missing....