This is the respective issue as https://www.drupal.org/project/drupal/issues/2245767, and would be a good addition to the features of our layouts system.

Problem/Motivation

Some blocks, like user login, should be shown on 403/404 response pages. Others, like the help block, should not.

Proposed resolution

Add a visibility setting to blocks that restricts visibility to any combination of 200/403/404 responses. Default this to show the block for all responses.

Perhaps in our case it also makes sense to add that visibility conditions to the layouts (besides blocks), so that if people really have the need for it, they can configure a different layout to be used based on response.

GitHub Issue #: 
6016