Can you pls enable DEBUG mode pls? Just set WP_DEBUG mode to true in wp-config.php file. There is probably an error that is causing this issue and we need to know the exact error. If you have access to the error log, pls send the same too.
I activated the default theme instead of Invent, disabled all plugins and still the issue persists – able to edit the post types but the list of posts/post types on the admin side simply refuses to show up – looks like there is a fatal error of PHP which is causing this.
At present, I did not notice any speed issues but we can improve the same by using caching plugin like WP Super Cache once we resolve the above one.