How to invalidate Breadcrumbs cache for child nodes on graphQl

I have for example Node A with alias node-a and Node B with alias node-a/node-b so on my Node B i have this breadcrumb Home > Node A > Node B

GraphQl result:

"breadcrumb": [
                {
                    "text": "Home",
                    "url": {
                        "path": "/",
                        "routed": true
                    }
                },
                {
                    "text": "Node A",
                    "url": {
                        "path": "http://example.com/node-a",
                        "routed": true
                    }
                },
                {
                    "text": "Node B",
                    "url": {
                        "path": "",
                        "routed": true
                    }
                }
            ]

But when i change Node A title i get always the same result (breadcrumbs not changed), but when i re-save the node A or clear cache the graphQl result change.

Here is what i have tried:

1. Clear graphQl cache (results and definitions)on node update:

     /**
     * Implements hook_ENTITY_TYPE_update().
     */
    function MYMODULE_node_update(EntityInterface $entity) {
      // Clear graphql cache.
      /** @var \Drupal\Core\Cache\CacheBackendInterface $graphql_results_cache */
      $graphql_results_cache = \Drupal::service('cache.graphql.results');
      $graphql_results_cache->invalidateAll();
      /** @var \Drupal\Core\Cache\CacheBackendInterface $graphql_definitions_cache */
      $graphql_definitions_cache = \Drupal::service('cache.graphql.definitions');
      $graphql_definitions_cache->invalidateAll();
    }

it doesn't work !

2. Clear cache of all child node on node update like this:

    /**
     * Implements hook_ENTITY_TYPE_update().
     */
    function MYMODULE_node_update(EntityInterface $entity) {
      $database = \Drupal::database();
      // Get the current node path alias.
      $alias = \Drupal::service('path_alias.manager')
        ->getAliasByPath('/node/' . $entity->id());
      // Get all node child of the current node.
      $child_nodes_alias = $database->select('path_alias', 'pa')->fields('pa', [
        'path',
        'alias',
      ])->condition('path', '/node/%', 'LIKE')
        ->condition('alias', $alias . '%', 'LIKE')
        ->execute()
        ->fetchAll();
      // Invalidate cache for each node child of current node.
      foreach ($child_nodes_alias as $alias_data) {
        $nid = explode('/', $alias_data->path)[2] ?? NULL;
        if ($nid && $nid != $entity->id()) {
          $tags = ['node:' . $nid];
          Cache::invalidateTags($tags);
          \Drupal::entityTypeManager()->getStorage('node')->resetCache([$nid]);
        }
      }
    }

it doesn’t work also

3. I combined the two previous ways it doesn't work too.

When i clear all caches on node update it works, but it's not the best way it impact site cache.

/**
 * Implements hook_ENTITY_TYPE_update().
 */
function MYMODULE_node_update(EntityInterface $entity) {
  drupal_flush_all_caches();
}

What is the best way to clear breadcrumbs cache, or child nodes without clear all site cache ?

Edit: Thank you @4K4 for your comment, i did tried to add CacheTags too breadcrumb but i didn’t work either !

/**
 * Implements hook_system_breadcrumb_alter().
 */
function MYMODULE_system_breadcrumb_alter(Breadcrumb &$breadcrumb, RouteMatchInterface $route_match, array $context) {
  // Append the current page title to the breadcrumb for non-admin routes.
  if ($breadcrumb && !\Drupal::service('router.admin_context')->isAdminRoute()) {
    $links = $breadcrumb->getLinks();
    foreach ($links as $link) {
      $parameters = $link->getUrl()->getRouteParameters();
      if ($parameters) {
        // Make sure the breadcrumb is updated when node title changes.
        $breadcrumb->addCacheTags(['node:' . $parameters['node']]);
        $breadcrumb->addCacheContexts(['url']);
      }
    }
  }
}

Note: Easy Breadcrumb module installed.

I don't know the caching implementation of GraphQL 3.x field plugins, but as far as I can tell this code (even after the latest update from 2018) doesn't collect the breadcrumb metadata because it only gets the links:

protected function resolveValues($value, array $args, ResolveContext $context, ResolveInfo $info) {
    if ($value instanceof Url) {
      $resolve = $this->subRequestBuffer->add($value, function () {
        $links = $this->breadcrumbManager->build($this->routeMatch)->getLinks();
        return $links;
      });

      return function ($value, array $args, ResolveContext $context, ResolveInfo $info) use ($resolve) {
        /** @var \Drupal\graphql\GraphQL\Cache\CacheableValue $response */
        $response = $resolve();
        $links = $response->getValue();

        foreach ($links as $link) {
          yield new CacheableValue($link, [$response]);
        }
      };
    }
  }

Shouldn't it get the breadcrumb object to add its cacheable metadata?

protected function resolveValues($value, array $args, ResolveContext $context, ResolveInfo $info) {
    if ($value instanceof Url) {
      $resolve = $this->subRequestBuffer->add($value, function () {
        $breadcrumb = $this->breadcrumbManager->build($this->routeMatch);
        return $breadcrumb;
      });

      return function ($value, array $args, ResolveContext $context, ResolveInfo $info) use ($resolve) {
        /** @var \Drupal\graphql\GraphQL\Cache\CacheableValue $response */
        $response = $resolve();
        $breadcrumb = $response->getValue();
        $links = $breadcrumb->getLinks();

        foreach ($links as $link) {
          yield new CacheableValue($link, [$response, $breadcrumb]);
        }
      };
    }
  }