It is important to make a backup of your Apple Music library so that you don't lose any music or videos that you have stored in your library in the event that you need to swap your machine or have your machine repaired.

To start, navigate to the finder and select the "Music" folder.

If you do not see the music folder on the left menu bar, select Finder from the top menu bar (next to the Apple logo), and click "Settings".

Click "Sidebar", then check the box next to the "Music" label and return to the normal Finder window.

Then, in Finder, right click on Music and select "Show in Enclosing Folder".

In the next window, right click on Music again, and select "Compress". This will create a "Music.zip" archive, which is what you will upload to your Google Drive. Rename the archive to "Music Backup" or something similar to better describe the file, then upload to Google Drive.

Depending on the size of your Music library, this could take some time to copy over to Google Drive.  Please make sure the copy is complete before you close or shutdown your comptuer.