docs(health): document health probe invariants and shutdown semantics

[NotThatKindOfDrLiz]

PR #93 changes health probe behavior, but some important invariants and ordering assumptions are only implicit in the code.

Requested follow-up:

• add a short comment near /healthz/startup explaining that it is only safe because the HTTP listener binds after Database::new().await and migrations complete
• add a short comment in the shutdown/readiness path explaining that DB checks are intentionally skipped during shutdown and the outer Shutting down response wins
• add a short comment noting that Cloud Run does not use readiness probes for traffic routing, so /healthz/ready is mainly useful for smoke tests and Kubernetes-style consumers

Context:

• These were raised as non-blocking inline review notes on PR Improve keycast health probes #93.

This is non-blocking for PR #93 but worth documenting so the current behavior does not depend on silent assumptions.

[sergey3bv]

Hey, @NotThatKindOfDrLiz, if you don't mind I will work on this issue

cc @rabble

[sergey3bv]

Hey, @NotThatKindOfDrLiz, I opened a PR, could you please take a look?

cc @rabble