Woocommerce modifying the html on the checkout page?

In your case, you don’t need to use the filter to inject the wrapper. Just override the checkout template file and put the wrapper at the line you need to.
In your question, you want to modify the billing form. So, it should be from this file
woocommerce/templates/checkout/form-billing.php. You can inject your wrapper at this line.

If you don’t know how to override the WooCommerce template. Please visit this link: https://docs.woocommerce.com/document/template-structure/

UPDATE: code sample.

foreach ( $fields as $key => $field ) {
    $field['return'] = true;
    $before = "";
    $after = "";

    switch ($key) {
        case 'billing_company':
            $before="<div class="address-wrapper">";
            break;
        case 'billing_postcode':
            $after="</div>";
            break;      
        default:
            # code...
            break;
    }

    echo $before . woocommerce_form_field( $key, $field, $checkout->get_value( $key ) ) . $after;
}