Health check with a happy path check

Following up from #50 (closed) and #59 (closed) we're checking if the server is healthy by checking if it'll respond { status: :unauthenticated }.

This can verify if the server is up and running, but cannot verify if it can really handle the events. This means it did not catch https://gitlab.com/gitlab-org/quality/triage-serverless/-/error_tracking/2455893/details while we're fixing it: !58 (merged)

We should pick a quick and fast happy path to check if it can handle actual events.