Refactor all Design Management mutations to have `errors` field

Summary

Currently, in Design Management application we only handle top-level GraphQL errors. However, as discussed in https://gitlab.com/gitlab-org/gitlab-ee/issues/13375 and https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/31622 we should be able to handle errors while they're sent as data.

This requires adding an errors field to every single mutation and adding an error handler to components where mutations are called.

Improvements

As a result, we will be able to display recoverable mutations to user even when data is sent.