docs: OpenAPI/Swagger documentation for REST API

[BillChirico]

The bot exposes a REST API with 8+ route files and 50+ endpoints, but there's no API documentation. This makes it hard for contributors or future dashboard work to know what's available.

Subtasks

• Generate OpenAPI spec — Add JSDoc-style annotations to route handlers, or write a standalone `openapi.yaml`
• Swagger UI — Mount `swagger-ui-express` at `/api/docs` (auth-gated)
• Document all endpoints: auth, config, guilds, health, members, moderation, community, webhooks, conversations (PR feat: AI conversations viewer with search and replay #121)
• Request/response schemas — Define TypeScript-like schemas for all request bodies and response shapes
• Error codes — Document all error responses (400, 401, 403, 404, 429, 500)
• Rate limit headers — Document `X-RateLimit-*` headers returned by rate-limited endpoints
• Authentication flow — Document Discord OAuth2 flow and session cookie requirements
• Public vs authenticated — Clearly mark which endpoints require auth and which are public

Technical Notes

• Consider `swagger-jsdoc` for annotation-based spec generation
• Alternative: hand-written OpenAPI 3.1 YAML (more control, less coupling)
• Gate Swagger UI behind auth in production

Acceptance Criteria

• All API endpoints documented with request/response schemas
• Swagger UI accessible at `/api/docs` for authenticated admins
• OpenAPI spec validates with `swagger-cli validate`

[coderabbitai]

🔗 Related PRs

#70 - feat: REST API layer for web dashboard [merged]
#120 - feat: public community page — leaderboards, showcases, and stats [closed]

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