Custom Post Type template stored in plugin folder not showing in post attributes dropdown

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The templates in your plugin don’t show up in your CPT because the templates are loaded from your theme (or child theme).

You’ll need to either

  1. Place the template in the root theme / child theme folder or
  2. Create a placeholder template file that “calls” the original

In the second case (which I’ve had to do a few times), I use something like this for the template in the theme / child theme:

<?php
/** 
 Template Name: My Custom Template
 */

include WP_PLUGIN_DIR.'/my-plugin/templates/my-template.php';

…while I’m sure there’s a better way at it; this works quite well. If you want to get really fancy, you could also add something to the plugin’s activation hook that copies this into the current theme.