iTunes 12.9.2.5 on macOS Mojave 10.14.2 drag and drop from Library to iPhone doesn't work

Is your device set up for iCloud Music Library as part of Apple Music or iTunes Match, or set up for automatic sycning? If not then as far as I am aware drag and drop from the iTunes library (not the media folder) to the device should work. Note that when manually managing an iPhone you are expected to do so from the same library each time. Trying to use a different library will generate an erase and sync warning.

You could try the following all-purpose steps for dealing with erratic device or sync behaviour (including the troublesome greyed out tracks and/or dotted circles of stalled transfers). They assume that all of the content you want on the device is in your library ready for restoring. If it isn't see Recover your iTunes library from your iPod or iOS device first. I would also recommend you copy everything out of the camera roll if you haven't already.

1. Backup device.
2. Restore as a new device.
3. Restore the backup you made earlier.

Use an encrypted backup (*) if you want to preserve passwords, Wi-Fi settings, web history and health data where appropriate. I also suggest syncing with a selection of playlists (unless you're using iCloud Music Library) rather than manually adding content as, if nothing else, the process above is easier to do if you ever have to go through it again.

(*) The downside with backup encryption is that if you forget the password when you need it again, which could be years later, you may need to invoke a workaround to turn off encryption as shown in Disable iOS backup encryption, which can only help if your device is in a state that can backup to iCloud, or runs iOS 11.

For added security you might also want to make an independent backup to iCloud and/or archive your current backup before you start.

FWIW I successfully used this method some time ago when Siri became unable to call contacts or play my music.

tt2

I understand why you want to use drag & drop, although I maintain that syncing with selected playlists gives you even more control if used properly. I'm running the latest build of iTunes and Mojave on my Mac. I have an iPhone configured for manual management with iTunes. I can drag & drop tracks, albums, or playlists from the library to the device. I'm afraid I think on this occasion Apple Support gave you incorrect information. If/when iTunes has trouble transferring content to a device the backup, restore as new device, restore backup approach has a good track record of resolving things, albeit that it really oughtn't to be necessary.

tt2