Now - since you have restricted some documents to certain groups, you need to manipulate the pimcore navigation renderer.
Navigation: Do not use the default nav builder extension (pimcore_build_nav). Just use the members_build_nav to build secure menus.
Otherwise your restricted pages will show up. This twig extension will also handle your navigation cache strategy.
{% set nav = members_build_nav(currentDoc, documentRootDoc, null, true) %}
{{ pimcore_render_nav(nav, 'menu', 'renderMenu', { maxDepth: 2 }) }}