Pass node field value to page.html.twig
You are probably a bit confused.

Variables are only available in specific templates. So the value of a field which is attached to an entity (like a content type) is only available in the template for that entity.

To make the body class field value available in a different template you need to


make a preprocess function for the template.
fetch the entity that has the field
expose it to the template.


For you it could look something like this.

function theme_name_preprocess_page(&amp;$variables) {
   // Define {{ body_class }}  in the template.
  if (!empty($variables['node']) &amp;&amp; !empty($variables['node']-&gt;field_body_class)) {
    $variables['body_class'] = $variables['node']-&gt;field_body_class-&gt;value;
  }
}