Introduce higher-level integration tests

Similar to https://gitlab.com/gitlab-org/gitlab-triage/-/issues/76 and https://gitlab.com/gitlab-org/gitlab-triage/-/merge_requests/82, I would like to have high-level tests which we can catch issues like !10 (merged) without adding a bunch of new unit tests.

The high-level integration test should take JSON as input as the event data, and then we verify with webmock to make sure it's making the right API request to fulfill the requirement.