How do I refresh “Post Last Modified Time”, as long as comment is updated to Approve status?

It’s easy, you can just use different hook to perform same action.

add_action( 'comment_approved_', 'update_post_time', 99, 2); // this will fire when comment is approved regardless of comment type 

Last underscore in action name is important comment_approved_ as normally after it goes comment-type if you need to hook to approval to specific comment types.

See https://core.trac.wordpress.org/browser/trunk/src/wp-includes/comment.php#L1748