Middle part of a page disappears and appears again after flushing all caches

Sometimes middle part of some page at our website may disappear and only header and footer are still displayed. The problem is always solved after flushing all caches.

Our html.html.twig loads templates a way like

{% include '@themename/header.html.twig' %}
{{ page }}
{% include '@themename/footer.html.twig' %}

And our page.html.twig loads an appropriate template depenging on the page path like

{% set path = path('<current>') %}
{% set pagePath = path|render|render %}
{% if pagePath == '/node' %} {# if homepage #}
{% include '@themename/homepage.html.twig' %}
{% else %}
{% include '@themename/innerpage.html.twig' %}
{% endif %}

We are not well familiar with Drupal caching so we don't know how exactly the problem is related to the caching. Maybe it's related somehow to render cache? As we use path|render|render in our page.html.twig. Or maybe it's related somehow to index.php which is appeared sometimes in the address bar?

The page template lists under General Utility Variables the is_front variable:

{% if is_front %}
  {% include '@themename/homepage.html.twig' %}
{% else %}
  {% include '@themename/innerpage.html.twig' %}        
{% endif %}

This should solve the problem, even if you visit the page by different URLs. You can avoid that as well, the Redirect module redirects out-of-the-box different paths of a page to a canonical one. Then the path based condition will be predictable, so this would be a second way to solve the problem.