How to add a column to edit posts area in admin panel?

What you see in the edit post columns is controlled by manage_posts_columns filter.

By playlist_id i assume you are looking for the post_id (since you mentioned playlists are simply custom post types). You can do so by using this code in your theme’s functions.php file:

if ( !function_exists('add_playlist_id_to_column') && function_exists('add_theme_support') ) {
    // Add our own column
    function add_playlist_id_to_column($cols) {
        $cols['playlist_id'] = __('PlayList ID','text-domain');
        return $cols;
    }
    // Get the post's ID
    function add_playlist_value($column_name, $post_id) {
        // If there is a post_id set, output it. Otherwise, print NONE.
        if ( $post_id ) {
            echo $post_id;
        } else {
            echo __('None','text-domain');
        }
    }
    // Hook to `manage_posts_columns` to run our function
    add_filter( 'manage_posts_columns', 'add_playlist_id_to_column' );
    add_action( 'manage_posts_custom_column', 'add_playlist_value', 10, 2 );
}