iTunes purchases on old account are stuck in my old phone.

I used to use my work email address as the Apple ID. Using that ID, I bought music on iTunes. Then I changed jobs and changed my Apple ID to a personal email address (rather than just changing the contact email for the old ID).

Recently, bought a new Mac. The the iTunes library on my new Mac, purchased after the change of ID, does not have any of the song purchased using the old ID even though I was synching it with my old iPhone.

Now I'm moving to a new iPhone. When I first set up the new phone, I transferred the contents of the old phone, and I got a message telling me that some items had been purchased using another user ID. It asked for the password for that ID, and I provided it, but when I entered the password I got an error message -- (SSServerError-Domain error 5001).

So the music purchased under the old ID is stuck there -- I can't transfer it to the new one. Without a backup, there's no obvious way to copy the files from old phone to the new one.

I see some third party software that claims to transfer music files from one device to another, but they have a cost and it's not clear that they'll do what I want.

Suggestions, please. Would setting up family sharing with he old ID work?