Use absolute URLs

Actually it's already possible:

/**
 * Implements hook_markdownify_entity_html_alter().
 */
function mymodule_markdownify_entity_html_alter(string &$html, array $context): void {
  $entity = $context['entity'];

  if ($entity && $entity->getEntityTypeId() === 'node') {
    $url = $entity->toUrl('canonical', ['absolute' => TRUE])->toString();
    $host = parse_url($url, PHP_URL_SCHEME) . '://' . parse_url($url, PHP_URL_HOST);

    $html = preg_replace_callback(
      '#(src|href)=["\'](/[^"\']+)["\']#',
      fn($m) => $m[1] . '="' . $host . $m[2] . '"',
      $html
    );

    $source = '<p>Source: ' . $url . '</p>';
    $html = $source . $html;
  }
}

Here I'm adding the source URL and absolute links.