Hi there,
you would have to use a Block Element Hook to add your social icons / social share plugin into the menu_bar_items hook.
That will mean one hook for social icons for the Frontpage
And a separate hook for social share icons ( which you will require a plugin for ) on your Posts
This will add them inside the Primary Navigation. Which will also show in the GP Sticky Navigation ( enabled in Customizer > Layout > Sticky Nav ). It will then require some CSS to show / hide the icons / menus etc. for the normal and sticky navs. We can help with the CSS once your have them in place.