The answer, as provided by the publisher via email, is as follows:

Manually Backing Up Your Bartender 5 Configuration  
    - Open Finder on your Mac.  
    - Press Command + Shift + G to open the “Go to Folder” dialog.  
    - Enter ~/Library/Preferences/ and press Enter.  
    - Locate the file named com.surteesstudios.Bartender.plist.  
    - Copy this file to a safe location (e.g., external drive, cloud storage).  
      Once you’ve copied this file, you’ll have a backup of your Bartender settings.  
  
2. Restoring or Transferring Settings: 
    If you need to restore (or transfer) your settings to another Mac:  
    - Replace the existing com.surteesstudios.Bartender.plist file in ~/Library/Preferences/ with your backed-up version.  
    - Restart Bartender to apply your restored settings.  
    - This process can also be used if you’re moving to a new Mac and want to keep your personalized Bartender layout and preferences.