How to add an optional VAT ID field to the checkout?

add_filter( 'woocommerce_checkout_fields' , 'checkout_address_details_fields' );
function checkout_address_details_fields( $fields ) {
    $fields['billing']['ct_invoice_taxid'] = array(
        'label'       => __('USt-Identifikationsnummer', 'woocommerce'),
        'placeholder' => '',
        'required'    => false,
        'class'       => array('form-row-wide'),
        'clear'       => true,
        'priority'    => 35,
    );

    return $fields;
}
 
add_action( 'woocommerce_checkout_update_order_meta', 'ct_invoice_save_fields' );
function ct_invoice_save_fields( $order_id ) { 
    if ( ! empty( $_POST['ct_invoice_taxid'] ) ) { 
       update_post_meta( $order_id, 'ct_invoice_taxid', sanitize_text_field( $_POST['ct_invoice_taxid'] ) ); 
    }  
}

add_action( 'woocommerce_admin_order_data_after_billing_address', 'ct_custom_checkout_field_display_admin_order_meta', 10, 1 ); 
function ct_custom_checkout_field_display_admin_order_meta($order){ 
    $taxid = get_post_meta( $order->get_id(), 'ct_invoice_taxid', true ); 
    if(!empty($taxid)){ 
        echo '<div class="clear"></div>'; 
        echo '<p>USt-Identifikationsnummer: '; echo '<span>'. $taxid . '</span>';  
        echo '</p>'; 
    } 
 }

add_filter( 'woocommerce_email_order_meta_fields', 'custom_woocommerce_email_order_meta_fields', 10, 3 );
function custom_woocommerce_email_order_meta_fields( $fields, $sent_to_admin, $order ) {
    $fields['ct_invoice_taxid'] = array(
        'label' => __( 'USt-Identifikationsnummer' ),
        'value' => get_post_meta( $order->id, 'ct_invoice_taxid', true ),
    );
    return $fields;
}