Pass a preprocess variable to a template?
At a glance it looks like you have a condition checking for:

if ($variables['field_name'] == 'field_language') {

but the template you are using is field--node--field-body.html.twig instead of field--node--field-language.html.twig.

To get it to pass to field body twig, you would need:

  if ($variables['field_name'] == 'field_body') {
    $variables['language'] = $variables['element']['#object']-&gt;get('field_language')-&gt;getString();
  }