What is the public flag for on custom Field sets?
From https://docs.civicrm.org/user/en/latest/organising-your-data/creating-custom-fields/#is-this-custom-field-set-public


  Is this Custom Field Set public?
  If a custom field set is marked as public, its fields will be shown on public-facing pages.
  
  For example, custom fields that should be shown on an event information page should belong to a field set marked as public. Custom fields that relate to administrative information about an event should be part of a field set that is not be marked as public.
  
  Note that the setting is at the Custom Field Set level and applies to all Custom Fields in the Set. Individual fields cannot be marked as public or not.