Add a hero image and text when a node goes from unpublished to published

I'm trying to add a hero image and text when a node goes from unpublished to published. The things include:

1. Add an image from my media library to a media field on the node
2. Add a page title to the node, drawing upon a field already saved on the node

I'm attempting to build a hook on hook_node_update() but it's not working. I'm not sure why.

The code I am using, part of the running_event_adding_header.module file, is the following.

namespace Drupal\Core\Field\EntityReferenceFieldItemList;
namespace Drupal\node\Entity;


/**
 * Implements hook_node_update()
 */
 
function running_event_adding_header_node_update(Drupal\Core\Entity\EntityInterface $entity) {
  // End function if the entity is not an event
  if ($entity->bundle() !== 'event') {
    return;
  }
  
  // End function if the event is not a running type of event (running events are '30' in my system)
  if ($entity->bundle() === 'event' && $entity->get('field_event_type')->getString() != '30') {
      return;
  }

  // Check if the new state is "published" and the old state was something other than "published".

  if ($entity->get('moderation_state')->getString() === 'published') {

    /**
    * Add hero image and text to running event page, if not already present
    * The hero image field is 'field_hero_image'
    * The hero text field is 'field_tagline'
    */

    if ($entity->get('field_hero_image')->isEmpty()) {
      $media = Media::load(53); // 53 is the media ID for the image I'm wanting to load on all running pages: .../media/53/edit
      $entity->set('field_hero_image', $media);
    }

    //'field_tagline' is the hero title field
    if ($entity->get('field_tagline')->isEmpty()) {
      $entity->set('field_tagline', $entity->label());
    }
    $entity->save();  
  }
}//close function

Updated code (29 July).

Per @sonfd's recommendation, this uses hook_node_presave(), but is still not changing the node pages:

<?php

namespace Drupal\Core\Field\EntityReferenceFieldItemList;
namespace Drupal\node\Entity;

//In the function below, I'm attempting to update
//'event' type nodes, specifically those with an event_type of '30'

//In those nodes, I'm attempting to use a Media library image 
//and use the page's title in the hero section


function running_event_add_default_node_presave(Drupal\node\NodeInterface $entity) {
  if ($entity->bundle() === 'event' && $entity->get('field_event_type')->toString()=== '30') {
    if ($entity->get('field_hero_tagline')->isEmpty()) {
      $entity->set('field_hero_tagline', $entity->label());
    }
    if ($entity->get('field_hero_image')->isEmpty()) {
      $media = Media::load(53); 
      $entity->set('field_hero_image', $media);
    }
  }



}