Hierarchy aggregated facet

For those looking for a work around now:

Create an aggregated facet (first or union) that includes the Taxonomy Term field from the entity types.
Create a search_api processor that inherits the addHierarchy processor, but add you fields manually.

namespace Drupal\your_module\Plugin\search_api\processor;

use Drupal\search_api\Plugin\search_api\processor\AddHierarchy as SearchApiAddHierarchy;

/**
 * @SearchApiProcessor(
 *   id = "your_module_hierarchy",
 *   label = @Translation("Index hierarchy - Aggregated fields"),
 *   description = @Translation("Adds to hardcoded aggregated fields the indexing of values along with all their ancestors for hierarchical fields (like taxonomy term references)"),
 *   stages = {
 *     "preprocess_index" = -45
 *   }
 * )
 */
class AddHierarchy extends SearchApiAddHierarchy {

  /**
   * {@inheritdoc}
   */
  protected function getHierarchyFields() {
    // Array: index => field => hiearchy as $entityTypeId-$property.
    $fields = [
      'search_index_name' => [
        'aggregated_field_name' => ['taxonomy_term-parent' => 'Taxonomy term » Term Parents'],
      ],
    ];
    return $fields[$this->index->id()];
  }

}

Then to translate the ID to display I couldn't think of anything better than a cut & paste of facets TranslateEntityProcessor hard coding the entity type (Taxonomy term) that you put into the aggregated field.

namespace Drupal\your_module\Plugin\facets\processor;

use Drupal\Core\Entity\EntityTypeManagerInterface;
use Drupal\Core\Language\LanguageManagerInterface;
use Drupal\Core\Plugin\ContainerFactoryPluginInterface;
use Drupal\Core\TypedData\TranslatableInterface;
use Drupal\facets\FacetInterface;
use Drupal\facets\Processor\BuildProcessorInterface;
use Drupal\facets\Processor\ProcessorPluginBase;
use Symfony\Component\DependencyInjection\ContainerInterface;

/**
 * Transforms the results to show the translated entity label.
 *
 * @FacetsProcessor(
 *   id = "translate_term_id",
 *   label = @Translation("Transform Term id into label"),
 *   description = @Translation("Show entity label instead of entity id. for an  integer known to be a Term ID."),
 *   stages = {
 *     "build" = 5
 *   }
 * )
 */
class TranslateTermIdProcessor extends ProcessorPluginBase implements BuildProcessorInterface, ContainerFactoryPluginInterface {

  /**
   * The language manager.
   *
   * @var \Drupal\Core\Language\LanguageManagerInterface
   */
  protected $languageManager;

  /**
   * The entity type manager.
   *
   * @var \Drupal\Core\Entity\EntityTypeManagerInterface
   */
  protected $entityTypeManager;

  /**
   * Constructs a new object.
   *
   * @param array $configuration
   *   A configuration array containing information about the plugin instance.
   * @param string $plugin_id
   *   The plugin_id for the plugin instance.
   * @param mixed $plugin_definition
   *   The plugin implementation definition.
   * @param \Drupal\Core\Language\LanguageManagerInterface $language_manager
   *   The language manager.
   * @param \Drupal\Core\Entity\EntityTypeManagerInterface $entity_type_manager
   *   The entity type manager.
   */
  public function __construct(array $configuration, $plugin_id, $plugin_definition, LanguageManagerInterface $language_manager, EntityTypeManagerInterface $entity_type_manager) {
    parent::__construct($configuration, $plugin_id, $plugin_definition);

    $this->languageManager = $language_manager;
    $this->entityTypeManager = $entity_type_manager;
  }

  /**
   * {@inheritdoc}
   */
  public static function create(ContainerInterface $container, array $configuration, $plugin_id, $plugin_definition) {
    return new static(
      $configuration,
      $plugin_id,
      $plugin_definition,
      $container->get('language_manager'),
      $container->get('entity_type.manager')
    );
  }

  /**
   * {@inheritdoc}
   */
  public function build(FacetInterface $facet, array $results) {
    $language_interface = $this->languageManager->getCurrentLanguage();

    $ids = [];

    /** @var \Drupal\facets\Result\ResultInterface $result */
    foreach ($results as $delta => $result) {
      $ids[$delta] = $result->getRawValue();
    }

    /** It's just this bit that has been changed **/
    // Default to nodes.
    $entity_type = 'taxonomy_term';
    /** Down to here **/

    // Load all indexed entities of this type.
    $entities = $this->entityTypeManager
      ->getStorage($entity_type)
      ->loadMultiple($ids);

    // Loop over all results.
    foreach ($results as $i => $result) {
      if (!isset($entities[$ids[$i]])) {
        unset($results[$i]);
        continue;
      }

      /** @var \Drupal\Core\Entity\ContentEntityBase $entity */
      $entity = $entities[$ids[$i]];

      // Check for a translation of the entity and load that instead if one's
      // found.
      if ($entity instanceof TranslatableInterface && $entity->hasTranslation($language_interface->getId())) {
        $entity = $entity->getTranslation($language_interface->getId());
      }

      // Overwrite the result's display value.
      $results[$i]->setDisplayValue($entity->label());
    }

    // Return the results with the new display values.
    return $results;
  }

}

Obviously this is going to fail if there are more than one entity type aggregated - but I can't think of a use case where that makes sense for hierarchy.