Steegle.One Intranet for Google Workspace
This technique may not be necessary any longer as you can now control access to a site via the published settings - see: Sharing and Publishing - new Google Sites
Publish your Google Site to your Google Workspace domain only
Create a Google Drive folder and share with your external viewers to the folder (either directly by email address or a group).
Find your site in Drive (either navigate or search for type:site)
Move the site into the shared Drive folder
The site will automatically inherit the view permission added to the Google Drive folder so those users who can view the folder will be able to view the site at the published URL.
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