language-attributes-variant-fix.php

<?php
/**
 * Language Attribute Variant Fix
 *
 * @package     language-attributes-variant-fix
 * @author      Bernhard Kau
 * @license     GPLv3
 *
 * @wordpress-plugin
 * Plugin Name: Language Attribute Variant Fix
 * Plugin URI: https://kau-boys.de
 * Description: Removes the language variant from the laguage attribute used on the HTML root element
 * Version: 0.1
 * Author: Bernhard Kau
 * Author URI: https://kau-boys.de
 * License: GPLv3
 * License URI: http://www.gnu.org/licenses/gpl-3.0.txt
 */

/**
 * Strips the language variant
 *
 * @param string $language_attributes The original language attributes value.
 *
 * @return string
 */
function language_attributes_variant_fix( $language_attributes ) {
	return preg_replace( '/lang="([\w]+-[\w]+)-[\w]+"/', 'lang="$1"', $language_attributes );
}
add_filter( 'language_attributes', 'language_attributes_variant_fix' );

function language_attributes_variant_fix( $language_attributes ) {
        return preg_replace( '/lang="([\w]+)-[\w]+[-\w]*"/', 'lang="$1"', $language_attributes );
}
add_filter( 'language_attributes', 'language_attributes_variant_fix' );

If we change the quantifier for the last segment, the function will work with de-DE als well as de-DE-formal.
I also selected the country code only, following the conversation on Twitter.