docs(health): update docs for /healthz/live, /healthz/ready, and /healthz/startup

[NotThatKindOfDrLiz]

PR #93 improves the health probe split, but the docs still describe the old /health behavior.

Requested follow-up:

• update docs/DEPLOYMENT.md
• update docs/MONITORING.md
• update docs/SIGNER_RELIABILITY_GUIDE.md
• remove or rewrite stale references that still describe /health as the liveness or startup endpoint
• document the intended roles of /healthz/live, /healthz/ready, and /healthz/startup

Context:

• This was called out as a non-blocking follow-up in the approving review for PR Improve keycast health probes #93.

This is non-blocking for PR #93 but should be cleaned up so deployment and monitoring docs match the new endpoint behavior.

[sergey3bv]

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

cc @rabble

[sergey3bv]

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

cc @rabble