How do I create custom 403/404/406/503 pages in Drupal 8? I am familiar with creating node and pointing to that specific node in basic site settings. How do i create this programmatically and package in features? Twig override?
To bundle and create programatically, you would need to create a custom module and inside that module: you could create a route for each specific page. That module could also update the config that is found in the system basic settings to use your custom pages.

Using this custom page you could call a custom page.html.twig and  override with the html you need.

Here are two resources: 


https://www.drupal.org/node/2116767
How do I update the configuration of a module?