Is there a preset CSS class when shopping cart isn’t empty?

You’ll need php for that… try this in your functions.php:

Detect if cart is empty and add class to body if is:

add_filter( 'body_class','my_custom_class' );
function my_custom_class( $classes ) {
    if ( WC()->cart->get_cart_contents_count() == 0 ) {
        $classes[] = 'my-emptycart-class';
    }

    return $classes;

}

Now you can use .my-emptycart-class in your CSS.