node_get_recent() is deprecated

node_get_recent() is unused in core and is now deprecated. Replacement is to use either views or EntityQuery to get the most recently changed nodes.

Before:

$latest_updated_nodes_array = node_get_recent(10);

After:

If you're only concerned with published nodes:

$nids = \Drupal::entityQuery('node')
  ->accessCheck(TRUE)
  ->condition('status', NodeInterface::PUBLISHED)
  ->sort('changed', 'DESC')
  ->range(0, 10)
  ->addTag('node_access')
  ->execute();
$latest_updated_nodes_array = !empty($nids) ? Node::loadMultiple($nids) : [];

If you're interested in including recent unpublished and draft nodes as well as published nodes, you'll want to replicate the code more like it was in its original form:

  $account = \Drupal::currentUser();
  $query = \Drupal::entityQuery('node');

  if (!$account->hasPermission('bypass node access')) {
    // If the user is able to view their own unpublished nodes, allow them
    // to see these in addition to published nodes. Check that they actually
    // have some unpublished nodes to view before adding the condition.
    $access_query = \Drupal::entityQuery('node')
      ->accessCheck(TRUE)
      ->condition('uid', $account->id())
      ->condition('status', NodeInterface::NOT_PUBLISHED);
    if ($account->hasPermission('view own unpublished content') && ($own_unpublished = $access_query->execute())) {
      $query->orConditionGroup()
        ->condition('status', NodeInterface::PUBLISHED)
        ->condition('nid', $own_unpublished, 'IN');
    }
    else {
      // If not, restrict the query to published nodes.
      $query->condition('status', NodeInterface::PUBLISHED);
    }
  }
  $nids = $query
    ->accessCheck(TRUE)
    ->sort('changed', 'DESC')
    ->range(0, 10)
    ->addTag('node_access')
    ->execute();

  $latest_updated_nodes_array = !empty($nids) ? Node::loadMultiple($nids) : [];

You may also wish to remove the status condition entirely and instead leverage just the ::accessCheck():

$nids = \Drupal::entityQuery('node')
  ->accessCheck(TRUE)
  ->sort('changed', 'DESC')
  ->range(0, 10)
  ->addTag('node_access')
  ->execute();
$latest_updated_nodes_array = !empty($nids) ? Node::loadMultiple($nids) : [];