How to sync Music from iPhone to Apple Watch?

I have a new iPhone 15 Pro running iOS 18.2 and a year-old Apple Watch 9 running WatchOS 11.2. The new iPhone will eventually replace an iPhone 13 Pro running iOS 18.1.1. After installing the .2 updates, I am seeing in Music on the Watch wrong album covers. The music on the iPhones originate from CDs that were synced to Macs via iTunes, then via Finder.

What I have discovered: There seem to be multiple Music libraries that can be selected on the iPhone, "My Library" and "Richard's Library". On the new iPhone "My Library" has the same wrong album covers as on the Watch, while "Richard's Library" does not. But setting the Library to "Richard's Library" in Music on the iPhone does seem to have any influence on which library Watch downloads its music from. On the old iPhone still running iOS 18.1.1 both libraries exist, but the album covers in "My Library" are not messed up.

Seems I need either a way to switch the two libraries on the iPhone 15 Pro or to specify in the Watch app on the iPhone which library on the iPhone to import music from.

On the Mac, which is still running Sonoma 14.7.2, I see no evidence of multiple Music libraries. In its library the album covers are alright.

It seems that I need some way to either switch the libraries in Music on the new iPhone or to tell the Watch which library on the iPhone to use.

This is a real mess. I've been "migrating" from the iPhone 13 Pro to the 15 Pro for the better part of two weeks now. Not a day goes by that I don't discover something that wasn't automagically migrated .

[Re-Titled by Moderator]