How to include a post type in the admin/backend?

First…

I’m changing the backend/admin …

Your description makes it sound like you are hacking Core. Don’t do that. It is a maintenance nightmare.

The action hook in_admin_header looks to be placed about where you want to put your content.

190 /**
191  * Fires at the beginning of the content section in an admin page.
192  *
193  * @since 3.0.0
194  */
195 do_action( 'in_admin_header' );

Use that hook to add your content.

function admin_content_wpse_144936() {
  echo 'howdy';
}
add_action('in_admin_header','admin_content_wpse_144936');

If you look at the 75 lines or so below that hook in the source you will see several other hooks that might be promising as well.

The admin_head-$hook_suffix hook could be used to give you pretty good control over when your content is added. For example:

function admin_content_wpse_144936() {
  echo 'howdy';
}

function add_admin_content_wpse_144936() {
  add_action('in_admin_header','admin_content_wpse_144936');
}
add_action('admin_head-edit.php','add_admin_content_wpse_144936');