Send email to author when content is published through scheduler

I have used Scheduler module with content moderation integration to publish a content automatically. It is perfectly working using the module. Now I want to add a functionality that once the content is published via cron, an email will be sent to the author of that particular content.

I have used hook_scheduler_publish_action to perform this action, but unfortunately I am facing some different scenario.

1. If I remove node publish code and keep only the mail sending code, the mail is fired.
2. If I remove the mail sending code and keep only node publish code, the node is published.
3. If I keep both, only mail is sent, content is not published.

Ref: https://git.drupalcode.org/project/scheduler/blob/8.x-1.x/scheduler.api.php

Below code is only publishing content, not sending email.

function MYMODULE_scheduler_publish_action(NodeInterface $node) {
  // node moderation state will be 'published'
  $node->set('moderation_state', 'published');
  $node->save();

  // email send to author
  $mail_params = array(
    'mail_subject' => 'run cron',
    'mail_body' => '<p>node published using scheduler</p>',
    'mail_to' => '[email protected]'
  );

  \Drupal::service('MYMODULE.common_service')->FunctionToSendEmail($mail_params);
}

Below code is only sending email, not publishing content.

function MYMODULE_scheduler_publish_action(NodeInterface $node) {  
  // email send to author
  $mail_params = array(
  'mail_subject' => 'run cron',
  'mail_body' => '<p>node published using scheduler</p>',
  'mail_to' => '[email protected]'
  );
  
  \Drupal::service('MYMODULE.common_service')->FunctionToSendEmail($mail_params);
  
  // node moderation state will be 'published'
  $node->set('moderation_state', 'published');
  $node->save();
}

That means this hook only perform the first action and ignores others.

Now my question is how will I perform multiple actions using this hook or is there any other procedure to do this?

Please help me. Thanks in advance.

The Scheduler Module itself do provide some events , which one of them is PUBLISH. So you can create an event subscriber in your module and listen to publish event like this:

class YourSchedulerEventSubscriber implements EventSubscriberInterface {
  public function publishAndSendMail(SchedulerEvent $event) {
  /** @var \Drupal\node\Entity\Node $node */
  $node = $event->getNode();
  $node->set('moderation_state', $node->publish_state->getValue());

  $event->setNode($node);

  $mail_params = array(
  'mail_subject' => 'run cron',
  'mail_body' => '<p>node published using scheduler</p>',
  'mail_to' => '[email protected]'
  );
  \Drupal::service('MYMODULE.common_service')->FunctionToSendEmail($mail_params); //Better to be sent as service argumnets
  }

  /**
   * {@inheritdoc}
   */
  public static function getSubscribedEvents() {
    // The values in the arrays give the function names above.
    $events[SchedulerEvents::PUBLISH][] = ['publishAndSendMail'];
    return $events;
  }
}