How to download personally owned cds from Mac to iPhone 16.

Hi

I own hundreds of old cds that i have previously burned to my Mac air. I also have lots of music from Apple Music on my iPhone 16.

When I got my iPhone 16 I did a phone to phone data transfer and my old iPhone 11 had both my burned cds and Apple Music available to listen to in the Apple Music app. However my old burned cds did not transfer to my iPhone 16 and instead are now greyed out on the iPhone 16 and some cds have two copies of songs only one of which will play.

I called Apple and the tech support did not know how to get the burned cds from my Mac to my iPhone without loosing all the Apple Music and playlists on my iPhone 16. (On my Mac book synch music is off so I have the burned cds and music I have downloaded from Apple Music only onto the Mac on the Mac)

How can I get my music on my iPhone 16 straightened out ie get the burned cds on the iPhone 16 without Apple Music writing over them, get rid of the greyed out songs and the duplicate songs on some albums that won’t play.

Thanks

mike