Add taxonomy parent to the body class

functions.php

/**
 * Add taxonomy parent to the body class
 * 
 * @param array $classes The current classes.
 * @return array New array with updated classes
 */
 function body_class_add_parent_taxonomy( $classes ) {
 
  if ( is_tax() ) {
    $taxonomy = get_queried_object();
    $parent_id = isset( $taxonomy->parent ) ? $taxonomy->parent : '';
    $parent_term = get_term( $parent_id, $taxonomy->taxonomy );
    
    $classes[] = $parent_term->slug . '-taxonomy';
  }
    
  return $classes;
}

add_filter( 'body_class', 'body_class_add_parent_taxonomy' );