tl;dr:

When I open Apple Music (v1.0.6.10), it lists only my old phone under devices . It does not show my new iPhone.

I generally don't use Apple Music, but I would like to put 2 songs (a friend recorded them for me, they're not like available in stores or whatever) that I have on my computer (macOS) on to my new phone. I suppose I don't really care whether I get them on there via Apple Music app or not.

How can I get these songs onto my iPhone?

More info:

I no longer possess the old iPhone that Apple Music seems stuck syncing with. I performed a factory reset before getting rid of it. The bottom of the UI in Apple Music on the mac says Syncing and when i click that, this super unhelpful Activity window opens that says Updating "<your old phone>"... and it has an X so that I could cancel that. Of course that X does not actually do anything. When I plug in my current iPhone, it does not show up in Apple Music. (It has previously asked me to trust the computer as in If your computer doesn't recognize your iPhone, iPad, or iPod, and I can see the iPhone in the System Information and in the Xcode Devices and Simulators windows.

What do I do?

It seems that maybe Force Quitting AMPDevice*Agent may have resolved this issue. Attempted to restart, and got some error about Finder blocking restart because of activity with iOS device. I saw my old iPhone (no longer in my possession) in the Finder, and wasn't sure what to do. I Force Quit that one task, and restart succeeded. On restart, Apple Music no longer listed my old phone and now listed my new one.

If it happens again, it might also have something to do with the number of authorized devices that you have associated with Apple Music. In Music on your Mac, go to Account then click "View My Account...". You'll then scroll down to the Downloads and Purchases section and click "Manage Devices". Make sure that your old iOS device (and any other unused devices) are removed from this list. Hopefully, it doesn't happen again.