When directly visiting https://wordpress.com/types/wp_template/{siteId} we see that the count endpoint works, but no post content is being returned for this post type. We should mirror the edit functionality that /wp-admin/edit.php?post_type=wp_template provides
Calypso

wp-admin

Note: this is now wp_template_part.
D34120-code will fix this
馃This works for me without any additional work...
Tested on one of my test sites right now: https://wordpress.com/types/wp_template_part/coponsa8cfse12.wordpress.com

Should we also want to show it in the menu, we can remove these lines:
@copons try doing it without your a8c superuser, it's passing some capability checks that will fail for mere mortals :)
We don't want it in the menu, which is why public was otherwise false.
This fix has been deployed