If you have previously backed up your Apple Music library to Google Drive as a ZIP file, follow these steps to restore your songs, playlists, and media to your MacBook.  If you need to back up your Apple Music Library, refer to this knowledge base article.

Download the “Music Backup.zip” file to the Desktop of your new computer.  Find the “Music Backup.zip”  file in the web browser, select the three dots at the end of your file, and select “Download” or find the file using Google Drive in a Finder window, and drag it to the Desktop.  Depending on the file size, the download may take some time.
 

Double-click the “Music Backup.zip” file to uncompress it.  When it is done, you will see a folder called “Music Backup” on your Desktop.

Open a Finder window and select the Music folder.  If you do not see the Music folder, go to Finder > Settings > Sidebar and check the box next to "Music".

Select all the files from the Music Backup folder and drag them into the Music folder. 

When it starts to copy, you will get a message stating that “An item named "Music" already exists in this location. Do you want to replace it with the one you're moving?”  Select the “Apply to All” checkbox in the bottom left corner, and select the “Replace” button to continue copying the files.
 

Once the files have been copied over, you can launch the Music App.  You should see your music library and playlists.

If you do not see your playlists in the Music App, go to File > Library > Import Playlist, then locate the .xml file in the Music folder.