Migrating to new iPhone: Save music and lists from iOS that are not sync'd with MacOS

This is a problem I (and others) have run into before. Often times, the music lists and selections we have on our iPhone can skew from what we have on our Macs. Because access to the music library is so restricted (for reasons I don't understand), I cannot easily just back up my data from the iPhone to a separate space. This is a problem.

It's not unusual for people to create lists and import music onto their iPhone over time. Sometimes, if you sync with your Mac, you'll send up with multiple playlists like "Playlist 1" and "Playlist 2" etc. There doesn't seem to be a clean way to do this, without access to the music library data.

I use programs like WALTR PRO to copy a song to my iPhone. It's handy. But this and playlist editing create a different environment, and I should be able to back that up separately.

In preparation for my new iPhone (in a week), I want to solve this dilemma. Has anyone a clever way to accomplish what I need?

Thanks!