\Drupal\entity_hierarchy\Storage\EntityTreeNodeMapperInterface - instead use the query builder factory.
$queryBuilder = \Drupal::service('entity_hierarchy.query_builder_factory')->get($fieldName, $entity->getEntityTypeId());
$childEntities = $queryBuilder->findChildren($entity)
->filter(RecordCollectionCallable::viewLabelAccessFilter(...));
\Drupal\entity_hierarchy\Storage\NestedSetNodeKeyFactory - there is no replacement, work directly with a Drupal entity and the query factory
\Drupal\entity_hierarchy\Storage\NestedSetStorage and \Drupal\entity_hierarchy\Storage\NestedSetStorageFactory - work with the query builder factory (\Drupal\entity_hierarchy\Storage\QueryBuilderFactory instead
We no longer use the previousnext/nestedset library, so e.g. value objects like \PNX\NestedSet\Node and \PNX\NestedSet\NodeKey no longer exist
See https://www.drupal.org/project/entity_hierarchy/releases/5.x-dev