iOS 13 screw-up - Songs not syncing
Music/iTunes syncing with iOS devices is indeed slightly screwed. From my diagnosis, it is because of iOS 13 update and has little to nothing to do with macOS Catalina update.



Fix:


Connect your iOS device to Mac.
Go to your device syncing app:


iTunes for pre-Catalina; and,
Finder for macOS Catalina.

Select the device you want to fix your music library on.
Go to the 'Music' tab in the device sync settings.
Uncheck 'Sync Music onto device name'.
Click 'Apply'.
For verification, eject the device and see that there is no song on your device now (except for maybe the content purchased from iTunes Store).
Plug the device back in and check the 'Sync Music onto device name'.
Click 'Apply'.
Wait to let the library sync to your device.


The missing songs should be on your device and the artwork must be restored as well.