Add term name to body class

test.theme

function THEME_preprocess_html(&$variables) {
  if ($variables['node_type'] == 'page') {
    $node_id = \Drupal::routeMatch()->getRawParameter('node');
    $node = Node::load($node_id);
    if ($term = $node->get('field_page_type')->entity) {
      $term_name = $term->get('name')->getString();
      switch ($term_name) {
        case 'My term':
          $variables['page_type'] = $term_name;
          break;
      }
    }
  }