You can set CSS color and background color to your custom order status displayed in admin order list this way:
add_action('admin_head', 'styling_admin_order_list' );
function styling_admin_order_list() {
global $pagenow, $post;
if( $pagenow != 'edit.php') return; // Exit
if( get_post_type($post->ID) != 'shop_order' ) return; // Exit
// HERE we set your custom status
$order_status="Dispatched"; // <==== HERE
?>
<style>
.order-status.status-<?php echo sanitize_title( $order_status ); ?> {
background: #d7f8a7;
color: #0c942b;
}
</style>
<?php
}
Code goes in function.php file of your active child theme (or active theme). Tested and works.