Improve adaptability of AIGW completions

This implements a series of improvements deemed necessary over the
implementation of prompt migrations
(https://gitlab.com/gitlab-org/gitlab/-/merge_requests/165884 and
https://gitlab.com/gitlab-org/gitlab/-/merge_requests/167364), in
regards to allowing feature teams to incorporate their own specific
behavior. Concretely, these changes accomplish the following:

- Allow signaling an error when processing the inputs
- Allow an early return when the AI action shouldn't be executed
- Facilitate overriding the response modifier
- Facilitate feature-specific error structures
- Allow post-processing the AIGW response before sending it to the
  modifier
- Notify callers when an unexpected error occurs