[M5] Write the deployment guide and production checklist

[igbopharaoh]

Tracking

• Milestone: M5 - Public Beta Readiness
• Suggested labels: priority:p1, type:docs, area:ops, milestone:public-beta

Context

Document how to operate PRGuard beyond a laptop, including GitHub App configuration and recovery procedures.

Scope

• Document deployment options for API, web, and Postgres.
• Document migrations and rollout strategy.
• Document GitHub App setup, webhook URL, permissions, and event subscriptions.
• Add a real test-repository smoke checklist.
• Add backup, rollback, and secret-rotation notes.

Acceptance criteria

• A maintainer can deploy a staging instance from the documentation.
• Smoke testing covers checks, labels, bot comments, dashboard, profile, and /claim.

Validation

• Follow the guide on a staging instance or conduct a dry run with an independent reviewer.

Definition of done

• Relevant Rust, API, or web tests pass.
• Documentation and runbook notes are updated when behavior changes.
• The pull request includes a concise manual verification note.