Incomplete iTunes music transfer from iPhone 11 to iPhone 16

I have about 3000 songs in my iTunes on my iphone 11 and macbook. These songs were purchased via the iTunes Store, uploaded directly from CDs, or purchased elsewhere online over the past 20+ years. I just purchased a new iPhone 16 and am trying to transfer all of this music to the new phone and for some reason it is only transferring some of the music. I've tried multiple times and each time, it transfers different songs. I have never had an Apple Music subscription and want to continue to avoid one. Any suggestions on how to successfully transfer the music to my new phone so that I can erase the old phone for trade it?

[Re-Titled by Moderator]