How to copy/clone menu of a node when clone with Entity Clone module?
Issue #2839833 has a proposal to add entity clone plugin to node entity to handle this special case.

Alternatively, we could use the event. Luckily Entity Clone module dispatches an event before &amp; after clone for the other modules to act. Here is the code for menu copy:

  // mymodule.services.yml

 mymodule.entity_clone.subscriber:
    class: Drupal\mymodule\EventSubscriber\EntityCloneSubscriber
    tags:
      - { name: 'event_subscriber' }


Subscribe to the post clone event:

&lt;?php

namespace Drupal\mymodule\EventSubscriber;

use Drupal\Core\Entity\EntityInterface;
use Drupal\entity_clone\Event\EntityCloneEvent;
use Drupal\entity_clone\Event\EntityCloneEvents;
use Drupal\menu_link_content\Entity\MenuLinkContent;
use Drupal\node\NodeInterface;
use Symfony\Component\EventDispatcher\EventSubscriberInterface;

/**
 * Crates menu item after node clone.
 */
class EntityCloneSubscriber implements EventSubscriberInterface {

  /**
   * Entity post clone handler.
   *
   * @param \Drupal\entity_clone\Event\EntityCloneEvent $event
   *   An event object.
   *
   * @throws \Drupal\Core\Entity\EntityStorageException
   */
  public function onPostClone(EntityCloneEvent $event) {
    $entity = $event-&gt;getEntity();

    // Act only on node clone.
    if (!($entity instanceof  NodeInterface)) {
      return;
    }
    $cloned_entity = $event-&gt;getClonedEntity();
    $values = menu_ui_get_menu_link_defaults($entity);

    // Copy menu item, if available.
    if (!empty($values['entity_id'])) {
      $this-&gt;cloneNodeMenuLinkContent($cloned_entity, $values);
    }
  }

  /**
   * Clones menu link content associated with the node.
   *
   * @param \Drupal\Core\Entity\EntityInterface $cloned_entity
   *   Cloned node.
   * @param array $values
   *   An array of menu link content values.
   *
   * @throws \Drupal\Core\Entity\EntityStorageException
   */
  protected function cloneNodeMenuLinkContent(EntityInterface $cloned_entity, array $values) {
    $menu_item = MenuLinkContent::load($values['entity_id']);
    $menu_name = $values['menu_name'];

    // Create new menu link content with original value.
    $cloned_menu_item = MenuLinkContent::create([
      'link' =&gt; ['uri' =&gt; 'entity:node/' . $cloned_entity-&gt;id()],
      'langcode' =&gt; $cloned_entity-&gt;language()-&gt;getId(),
    ]);
    $cloned_menu_item-&gt;enabled-&gt;value = $menu_item-&gt;isEnabled() ? 1 : 0;
    $cloned_menu_item-&gt;title-&gt;value = trim($cloned_entity-&gt;getTitle());
    $cloned_menu_item-&gt;description-&gt;value = trim($values['description']);
    $cloned_menu_item-&gt;menu_name-&gt;value = $menu_name;
    $cloned_menu_item-&gt;parent-&gt;value = $values['parent'];
    $cloned_menu_item-&gt;weight-&gt;value = isset($values['weight']) ? $values['weight'] : 0;
    $cloned_menu_item-&gt;save();
  }

  /**
   * {@inheritdoc}
   */
  public static function getSubscribedEvents() {
    $events = [];
    $events[EntityCloneEvents::POST_CLONE][] = ['onPostClone', 200];
    return $events;
  }

}