Loco Translate: Custom Post and Custom Taxonomy Labels not translated in wp-admin menu

For anyone having the same trouble, I am now using a workaround from the accepted answer on the following question: https://wordpress.stackexchange.com/a/30723/181214

I am using the solution beyond the “EDIT: Another Option” which is working fine for slugs, names, singular names etc.

function get_labels() {
    // return a default slug
    if(!defined('WPLANG') || !WPLANG || 'de_DE' == WPLANG) return array('slug' => 'produkt', 'name' => 'Produkte', 'singular_name' => 'Produkt');

    $slugs = array(
        'en_US' => array('slug' => 'product', 'name' => 'Products', 'singular_name' => 'Product'),
        'en_UK' => array('slug' => 'product', 'name' => 'Products', 'singular_name' => 'Product'),
        'de_DE' => array('slug' => 'produkt', 'name' => 'Produkte', 'singular_name' => 'Produkt'),
        'de_CH' => array('slug' => 'produkt', 'name' => 'Produkte', 'singular_name' => 'Produkt'),
        'fr_FR' => array('slug' => 'produit', 'name' => 'Produits', 'singular_name' => 'Produit'),
        'es_ES' => array('slug' => 'producto', 'name' => 'Productos', 'singular_name' => 'Producto')
    );

    return $slugs[WPLANG];
}

function product() {
    $labels = get_labels();

    register_post_type('product',
        array(
            'labels'      => array(
                'name'          => $labels['name'],
                'singular_name' => $labels['singular_name'],
            ),
            'public'      => true,
            'has_archive' => true,
            'show_ui' => true,
            'rewrite' => array(
                'slug' => $labels['slug']
            ),
            'show_in_menu' => true,
            'supports' => array(
                'title',
                'post-thumbnail',
            )
        )
    );
}
add_action('init', 'product');