plex Music media library not updating after mp3 tags changed

This particular behaviour can be changed quite easily if you re-order the metadata agents, so that embedded metadata can get overridden by the online metadata sources:
Go to

  • Settings - Server - Agents - Shows - TheTVDB

In there, grab the line ‘Local Media Assets’ with your mouse and drag it downwards, so it ends up being at the bottom of the stack of active agents.
Repeat the same under

  • Settings - Server - Agents - Shows - TheMovieDatabase
  • Settings - Server - Agents - Movies - Plex Movie
  • Settings - Server - Agents - Movies - TheMovieDatabase

After doing the above change, you only need to Refresh Metadata. A complete Plex Dance is usually not necessary (unless the nonsensical embedded metadata have caused a mismatch).