How to render a node with absolute URL to use in a mail?
Two possible approaches:


Find the URLs in preprocess targeting this specific view mode and apply setAbsolute(), see for example How do I render the absolute URL of a referenced entity in a simplenews newsletter? 
Apply a regex on the rendered output $html or use Html::transformRootRelativeUrlsToAbsolute() like added recently to the core MailManager:

$html = Markup::create(Html::transformRootRelativeUrlsToAbsolute((string) $html, \Drupal::request()-&gt;getSchemeAndHttpHost()));


Source: https://git.drupalcode.org/project/drupal/commit/530f7ac


By the way, use instead of render() the method renderPlain(), see How to deal with Bubbleable Metadata when there&#39;s no rendering context and no render array