User Profile should be usable without public visibility

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Is your feature request related to a problem? Please describe.
The new user profile feature is a valuable addition to every cloud, but it's sad that it always is publicly visible. The most private clouds are just that: private. And so no information should be visible to the public.

The current profile is a choice between "make some information visible to the public" or "don't use profiles". But profiles are useful for private use inside the cloud, too.

Describe the solution you'd like
The user profile as a whole should at least get an option "only visible to logged in users". Even better, the administrator should be able to configure the visibility for all accounts.

So I request:

• a user option to make the profile invisible to the public
• administrator options
  • make no profile visible to the public and the user could not change this
  • make no profile visible to the public by default and the user can change it afterwords
• for updates make all profiles not visible to the public and the user could change this

Describe alternatives you've considered

Additional context

No files or tests are named in the issue. Start by tracing the user-profile visibility flow and its administrator settings, then compare the implementation with the requested user, default, enforced, and update behaviors; done means the listed visibility policies work for users and administrators.