Wordpress - Page editor missing Templates drop down

Maybe this will help.

<?php 
/*
Template Name: Featured
*/
get_header(); ?>

Regular code here...

<?php get_footer(); ?>

If one theme works you could try replacing the files in the broken theme and test which file or files are broken. But first save the old files in a separate folder as a backup. Then you would know which file or files are broken pretty quickly.

By default Wordpress theme directory have not any template page then template page dropdown is invisible so follow the below instruction.

For display template page dropdown in wordpress admin page you need to create one template page in your theme directory code is below

<?php 
/*
Template Name: template home 
*/
?>

By creating this template file in your theme directory you can see template dropdonw is visible in admin page.

If you're not seeing the dropdown at all you might need to reload your theme. Try switching to another theme and then switching back.