This snippet adds the entity type id to the html body tag classes when on the canonical entity page.
/**
* Implements hook_preprocess_HOOK() for HTML document templates.
*/
function yourtheme_preprocess_html(&$variables) {
// If this is the canonical entity route, add the entity type id to the body
// tag classes. Also add 'canonical' as an extra identifier.
if (preg_match('/entity\.(\w+)\.canonical+/', Drupal::routeMatch()->getRouteName(), $matches)) {
$variables['attributes']['class'][] = $matches[1];
$variables['attributes']['class'][] = 'canonical';
}
}