Show total search result count
The search queries of Drupal 8 use the global pager. The total results count is available within its global $pager_total_items variable.

So the easiest way of showing the amount of total items is using this variable within a hook_preprocess_HOOK() of your template in your *.theme file.

For example, if you'd like to use the total results count within the item-list--search-results.html.twig, HOOK needs to be replaced by its theme hook item_list__search_results:

/**
 * Implements hook_preprocess_HOOK() for item_list__search_results.
 */
function mytheme_preprocess_item_list__search_results(array &amp;$variables) {
  // The $pager_total_items variable is a global
  // array keyed by the pager element increments.
  global $pager_total_items;

  // Assuming you have one paged list on your page only,
  // the element's key should be 0.
  $variables['total_items_count'] = isset($pager_total_items[0]) ? $pager_total_items[0] : 0;
}


Then you can access this variable like {{ total_items_count }} within the template.