if current_node is in menu, do something in theme.inc I'm trying to check if the current node (of a specific content type) has been added to a menu (using the "Provide a menu link" in the node edit GUI). 

if it has, I need to set a variable in .theme.inc, using THEME_preprocess_page.

I've been digging through drupal.org docs and found those two questions find Menu Settings of node, given URL alias (or node ID) and Get menu item of a node seem relevant but not quite right.
To set if the node has menu link you can use menu_ui_get_menu_link_defaults function from menu_ui.module something like:

/**
 * Implements hook_preprocess_HOOK().
 */
function YOUMODULE_preprocess_page(&amp;$vars) {
  /** @var \Drupal\node\Entity\Node $node */
  if ($node = \Drupal::routeMatch()-&gt;getParameter('node')) {
    // Get the default menu link.
    $defaults = menu_ui_get_menu_link_defaults($node);
    if ($defaults['id']) {
      // It has a menu
     // set your variable here.
    }
    else {
      // It has no menu link
      // It mean Provide a menu link not checked
    }
  }
  }