find Menu Settings of node, given URL alias (or node ID) In the Drupal 8 screen for editing a node, we have these two sections:

URL Path Settings &gt; URL alias
Menu Settings (Menu link title, Description, Parent item, Weight)

How, given the URL alias of a node, can we get those Menu Settings, particularly the Menu link title?
This may break down into two separate problems:

finding the node ID from the URL alias
finding the Menu Settings from the node ID

and in fact I would be thrilled at a solution to either one, even as a high-level explanation.
I would go into detail about how I've attempted to answer this question already, and the services &amp; classes that appear to be relevant, but I don't want to post a complicated-looking question.  If data is that easy to put into those basic fields in the UI, it should at least be possible for some module code to get it back out.
Comments in my question getting URL from Route: breaks in localhost subdirectory have clarified that the solution of @4k4 is absolutely the right way to get the alias from the current path.  But the alias is not as useful as I thought in applying suggestion (@Ivan Jaros) to use entityQuery to take it the rest of the way, since the current path is able to match the link.uri field of menu_link_content, except for a leading slash in the pathname and the entity: protocol:

$current_path = \Drupal::service('path.current')-&gt;getPath();
$system_uri = 'entity:' . trim($current_path, '/');

$query = \Drupal::entityQuery('menu_link_content')
  -&gt;condition('link.uri', $system_uri)
  -&gt;condition('menu_name', 'main');

$result = $query-&gt;execute();
$menu_link_id = (!empty($result)) ? reset($result) : FALSE;

if ($menu_link_id) {
  $menu_link = MenuLinkContent::load($menu_link_id);
  $menu_link_title = $menu_link-&gt;getTitle();
} else {
  drupal_set_message(t('no Menu Link Content for ID that we found...'), 'error');
}