How to make a check that my entity title field is written to needed database table and that no other field is written there?

I have an entity called Entity Product. And this entity has a form, if you change the Title field in this form, Drupal will automatically save the new value of this field in the appropriate table in the database, but in addition, I also save the change of the Title field in the form to another database table product_product by creating a _custom_product_save_title function. It is necessary. And this function is called in the hook_ENTITY_TYPE_update() which tracks changes in Entity Product.

I need to add a check to see if the title is saved and if other fields are not saved. Please tell me what such a check should look like and where exactly should it be in the code?

function _custom_product_save_title($custom_product_id, $entity_product_title) {

  if (isset($fields['url']) && $fields['url'] == '') {
    if (isset($fields['name'])) {
      $fields['url'] = strtolower(str_replace(' ', '-', $fields['name']));
    }
  }
  $id = $form_state->getValue('cid');
  if (!empty($form_state->getValue('cid'))) {
    $query = $this->connection->update($this->getTableName())
      ->condition('cid', $form_state->getValue('cid'));
  }
  else {
    $query = $this->connection->insert($this->getTableName());
  }
  $result = $query
    ->fields($fields)
    ->execute();
  if (!$id) {
    $id = $result;
  }
 
  Cache::invalidateTags([
    "product:" . $form_state->getValue('cid'),
  ]);

  Cache::invalidateTags([
    "product:$custom_product_id",
  ]);

  if (!$custom_product_id) {
    Cache::invalidateTags([
      "product_list",
    ]);
  }

}

/**
 * Implements hook_ENTITY_TYPE_update().
 */
function product_admin_node_update(\Drupal\Core\Entity\EntityInterface $entity) {
  if ($entity->bundle() == 'product') {
    $custom_product_id = $entity->get('field_product_cid')->value;
    $entity_product_title = $entity->getTitle();
    _custom_product_save_title($custom_product_id, $entity_product_title);
  }
}

After debugging the code using xdebug, I see the following structure of what comes in the standard argument $entity of the hook:

$entity
  fields
    field_product_cid
    field_second
    .....
    title
      x-default
        list
          0
            values
              value = “My title”