How do I programmatically publish the latest revision?

1. My workflow is draft and publish.
2. I create and publish a page.
3. I create a draft of the page.

There is now the published page, but the latest revision is the draft.

How do I programmatically set as published the latest revision?

This code publishes the node.

$node = Node::load(nid);
// Publish and save the node.
if ($node->hasField('moderation_state')) {
  $node->set('moderation_state', 'published');
}
$node->setPublished();
$node->save();

The node is already published. I want to publish the draft/latest revision of the node.

This query has some possibilities.

// Publish the draft of a node.
$query = \Drupal::database()->select('content_moderation_state_field_revision', 'cm');
// $query->fields('cm', ['moderation_state']);
$query->fields('cm');
$query->condition('cm.content_entity_id', $node->id());
$query->condition('cm.moderation_state', 'draft');
$result = $query->execute();
$record = $result->fetchAssoc();
print_r($record);

Since nodes can have more than one draft, I could add a LIMIT and an ORDER BY to the query. Simply changing the moderation_state in the content_moderation_state_field_revision table and rebuilding the cache doesn't publish the latest revision.

This code, altered slightly from EntityModerationForm.php worked once, but then didn't work again.

/** @var \Drupal\Core\Entity\ContentEntityStorageInterface $storage */
$storage = \Drupal::entityTypeManager()->getStorage($node->getEntityTypeId());
$entity = $storage->createRevision($node, $node->isDefaultRevision());

$new_state = 'published';

$entity->set('moderation_state', $new_state);

if ($entity instanceof RevisionLogInterface) {
  $entity->setRevisionCreationTime(\Drupal::time()->getRequestTime());
  $entity->setRevisionLogMessage('Draft created automatically');
  $entity->setRevisionUserId(\Drupal::currentUser()->id());
}
//    $node->setNewRevision(FALSE);
$entity->save();