To restore your library, you will need to copy your Music folder (that you previously backed up) from Google Drive to your new laptop.

Open the Apple Music app and agree to any user agreements, then close the program.

Open the Finder and click on the Music section on the left.  If you do not see Music, go to Finder --> Preferences --> Sidebar and check Music.

Then drag your Music folder to the Music Section in the Finder.

If a dialogue box comes up asking if you want to replace the folder, click replace. 

While holding down the OPTION key on your keyboard, open the Music App again.  You will be prompted to choose a Music library.  Click Choose Library.

Browse to your Music folder and select the Music Library.musiclibrary file, then click "Choose."

Your music will now appear in the Music App.