How to update an existing drupal 8 site setting field with a hook update

YOUR_MODULE_NAME.install

/**
 * @file
 * Install, update and uninstall functions for the YOUR_MODULE_NAME module.
 */

/**
 * Implements hook_update_N().
 *
 * Update field_example on the my_example_setting site
 * setting to have all the term_example taxonomy terms selected.
 */

function YOUR_MODULE_NAME_update_8001(&$sandbox) {
  // Query the my_example_setting site settings to get their id's.
  $my_example_setting_ids = \Drupal::entityQuery('site_setting_entity')
    ->condition('type', 'my_example_setting')
    ->execute();

  // Load the application cta column entities using their id's.
  $my_example_setting_entity = \Drupal::entityTypeManager()
    ->getStorage('site_setting_entity')
    ->loadMultiple($application_cta_columns_ids);

  // Load the term_example taxonomy terms and put them into $terms
  // data array, which holds the term id's.
  $vid = 'term_example';
  $terms = \Drupal::entityTypeManager()->getStorage('taxonomy_term')->loadTree($vid);
  $terms_data = [];
  foreach ($terms as $term) {
    $terms_data[] = [
      'target_id' => $term->tid,
    ];
  }

  // For each my_example_setting, set the field data for
  // field_example to equal the $term_data array and save it.
  foreach ($my_example_setting_entity as $entity) {
    $entity->set('field_example', $terms_data);
    $entity->save();
  }

}