We previously implemented the `timed_out` count in
https://gitlab.com/gitlab-org/gitlab/-/merge_requests/53955/diffs
but it had to be reverted due to it not being able to handle an empty
response body
https://gitlab.com/gitlab-com/gl-infra/production/-/issues/3623
https://gitlab.com/gitlab-org/gitlab/-/merge_requests/54053 .

It was very easy to reproduce the problem observed in that by simply:

1. Visit `Admin > Settings > Preferences`
2. Update the email additional attributes
3. Save

This problem will actually happen when updating anything in the admin
UI.

This was quite surprising as we have tonnes of tests that go down this
code path throughout GitLab. As such it was very strange to not see a
single test failure outside of these QA tests that ran against staging.
It turns out the reason is that this code only runs when
`SafeRequestStore` is active otherwise the interceptor logic is skipped.
It turns out that none of our tests that execute these code paths had
the `SafeRequestStore` active. In an effort to reduce the risk of this
happening I've actived the `request_store` in the `helper_spec.rb` which
covers many of the Elasticsearch queries we execute which would have
actually caught this problem

Additionally I've updated the unit test with this new specific case and
another slightly similar case of error responses just to be safe.