Code snippet that can be used to get taxonomy term depth in Drupal 8.
$parents = \Drupal::entityTypeManager()->getStorage('taxonomy_term')->loadAllParents($term->id());
$depth = count($parents);
and to get the parent tid of a taxonomy term in Drupal 8 you can use this:
$parent = \Drupal::entityTypeManager()->getStorage('taxonomy_term')->loadParents($termId);
$parent = reset($parent);
You can simply use the $parent->id() method to get your parent tid.
