How to get tags outside of loop for specific page I’m on?

First you need to get the ID of the page/post/content you’re viewing. Then, you can call get_the_terms() and pass it that ID so it knows you want the tags for that specific piece of content.

<?php
$mtags = get_the_terms( get_queried_object_id(), 'custom_tag' );
?>

There isn’t an orderby parameter, so you may need to sort the array afterward if you want them in a specific order.