Metatag only works if you've added a custom tag on the source.

This isn't a robust-enough solution to be a patch, but here's the ImportProcessor I'm using in my custom module if it's useful for other people:

<?php

declare(strict_types=1);

namespace Drupal\mymodule\Plugin\EntityShareClient\Processor;

use Drupal\Core\Form\FormStateInterface;
use Drupal\Core\Plugin\PluginFormInterface;
use Drupal\entity_share_client\ImportProcessor\ImportProcessorPluginBase;
use Drupal\entity_share_client\RuntimeImportContext;
use Symfony\Component\DependencyInjection\ContainerInterface;

/**
 * Import book structure.
 *
 * @todo This can be deprecated if
 * https://www.drupal.org/project/entity_share/issues/3441672 is fixed.
 *
 * @ImportProcessor(
 *   id = "metatag_importer",
 *   label = @Translation("Use Server Canonical link"),
 *   description = @Translation("Get the Canonical url from the Metatag attribute on the Server."),
 *   stages = {
 *     "prepare_importable_entity_data" = 20,
 *   },
 *   locked = false,
 * )
 */
class MetatagImporter extends ImportProcessorPluginBase implements PluginFormInterface {

  /**
   * The entity type manager.
   *
   * @var \Drupal\Core\Entity\EntityFieldManagerInterface
   */
  protected $entityFieldManager;

  /**
   * {@inheritdoc}
   */
  public static function create(ContainerInterface $container, array $configuration, $plugin_id, $plugin_definition) {
    $instance = parent::create($container, $configuration, $plugin_id, $plugin_definition);
    $instance->entityFieldManager = $container->get('entity_field.manager');
    return $instance;
  }

  /**
   * {@inheritdoc}
   */
  public function buildConfigurationForm(array $form, FormStateInterface $form_state) {
    return $form;
  }

  /**
   * {@inheritdoc}
   */
  public function prepareImportableEntityData(RuntimeImportContext $runtime_import_context, array &$entity_json_data): void {
    if (isset($entity_json_data['attributes']['metatag'])) {
      // Find out if there's a Metatag type field on the node.
      $parsed_type = explode('--', $entity_json_data['type']);
      $entity_type_id = $parsed_type[0];
      $entity_bundle = $parsed_type[1];
      $entity_fields = $this->entityFieldManager->getFieldDefinitions($entity_type_id, $entity_bundle);
      $metatag_field = NULL;

      foreach ($entity_fields as $id => $field) {
        if ($field->getType() === 'metatag') {
          $metatag_field = $id;
        }
      }
      if ($metatag_field && $entity_json_data['attributes'][$metatag_field] === NULL) {
        foreach ($entity_json_data['attributes']['metatag'] as $value) {
          if (isset($value['attributes']['rel']) &&  $value['attributes']['rel'] === 'canonical') {
            $entity_json_data['attributes'][$metatag_field] = [
              'value' => [
                'canonical_url' => $value['attributes']['href'],
              ],
            ];
          }
        }
      }
    }
  }

}

This would be enabled as a plugin called "Use Server Canonical link" at the import config level under `/admin/config/services/entity_share/import_config`.