Sync music tags to PC
If you are open to alternative ways of syncing, you might want to take a look at e.g. FolderSync:

 

It enables you to sync selected locations with different cloud services, but also with your local "home network". You can set it to automatically synchronize, or have it done manually on-demand.

For your issue, you could set either the base directory of your music to completely synchronize between your Android device and your PC, or chose selected directories. So when you updated some tags, only those files should be "copied to the other side", as the others have not changed. Same applies if you add new music files.

There are some other apps in the playstore doing the same job, just in case you want some alternatives. One of them would be FTPSyncX which, other than its name suggests, also handles different protocols (Samba/Windows Shares, SFTP/SSH, FTPS).