In static websites in general restricting content is very problematic.
You can try to use solutions like this: https://docs.netlify.com/visitor-access/identity/ but please remember that Publii has no built-in support for this at this moment, so I do not know if it will be possible to make it working with Publii site.
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Yes, i thought the same thing about the static websites. Probably (because i’m not a web developer) a solution if you don’t want to change the CMS can be to integrate another CMS with restricted pluging linking a page or a menu to the new site.