get_post_meta remains empty while looping all menu items and using the ID

You are sending the ID of the menu item not the ID of the page try using url_to_postid() like this:

<?php
 $array_menu = wp_get_nav_menu_items('header-menu');
    $menu = array();
    foreach ($array_menu as $m) {
        if (empty($m->menu_item_parent)) {
             ?>
             <h4><a href="https://wordpress.stackexchange.com/questions/257249/<?php echo $m->url;?>"><?php echo $m->title;?></a></h4>
             <p>
                <?php global $wp_query;
                 $pageID = url_to_postid( $m->url );  
                 echo get_post_meta($pageID, 'meta_box_subtitle', true); 
                ?>
             </p>
<?php       
        }
    }
?>