Alternatives for Copying Music [Uploaded into Music App] to iPhone

I have spent many hours with Apple Tier II Tech Support to try to get my CDs uploaded to the Music app on my Mac Mini (Sonoma 14.6.1)onto my iPhone 14 Pro (17.6.1). Several weeks ago, I uploaded most of my CD collection to this Mac mini, then sync'd the entire music library to my iPhone. This seemed to work but, over time, many CDs have disappeared from the iPhone and I am not able to get them back using the Sync function in Finder. We have run out of ideas, so am looking for third party alternatives to accomplish this. Has anyone here found such an App?

Thanks in advance.

Everett