Add base field to existing entity type

module_name.install

/**
 * Add the entity_type field_name field.
 */
function module_name_update_9001() {
  $type_manager = \Drupal::entityTypeManager();
  $type_manager->clearCachedDefinitions();
  $entity_type = $type_manager->getDefinition('entity_type');
  $storage_definition = EntityTypeClass::baseFieldDefinitions($entity_type);

  \Drupal::entityDefinitionUpdateManager()->installFieldStorageDefinition(
    'field_name',
    $entity_type->id(),
    'entity_type',
    $storage_definition['field_name']
  );
}