docs(api): add public API documentation site (Astro Starlight)

## Changes
- Add narrative API documentation in docs/api-content/ (introduction,
  quickstart, authentication, conventions, errors, rate limiting)
- Scaffold Astro Starlight site at docs/api/ that consumes prose from
  the sibling api-content folder and auto-generates the endpoint
  reference from server/openapi.json via starlight-openapi
- Wire Checkmate brand color (#13715B) into Starlight via custom CSS
- Add vercel.json so the docs site deploys cleanly as an Astro project
  with root directory docs/api/

## Benefits
- Public API docs ready to publish at checkmate.so/docs
- Endpoint reference stays in sync with the OpenAPI spec automatically
- Zero third-party SaaS dependency: site is fully self-hosted on Vercel
- Contributors edit plain markdown; no Astro knowledge needed for prose

docs/api-content/api-reference/overview.md

@@ -0,0 +1,47 @@
+---
+title: API reference overview
+description: All endpoints, grouped by resource. Auto-generated from the OpenAPI spec.
+---
+
+# API reference
+
+The full machine-readable specification is at [`server/openapi.json`](https://github.com/bluewave-labs/Checkmate/blob/develop/server/openapi.json). Mintlify renders an interactive reference from it — each endpoint below is fully documented with request/response schemas, examples, and a built-in "Try it" form.
+
+## Endpoint groups
+
+| Group | Description |
+|---|---|
+| **auth** | Register, log in, password recovery, manage users |
+| **invite** | Send and redeem team invites |
+| **monitors** | Create, update, pause, and delete monitors |
+| **checks** | Read individual check results and team-wide summaries |
+| **incidents** | List, filter, and resolve downtime incidents |
+| **maintenance-window** | Schedule maintenance windows to silence checks |
+| **notifications** | Configure email, Slack, Discord, and webhook channels |
+| **status-page** | Manage public status pages |
+| **geo-checks** | Multi-region check results |
+| **logs** | Audit and operational logs |
+| **settings** | Global Checkmate settings |
+| **queue** | Background-job queue health (operational) |
+| **diagnostic** | System health and version info |
+
+## Authentication
+
+Every endpoint except the unauthenticated auth/recovery routes requires:
+
+```
+Authorization: Bearer <jwt>
+```
+
+See [Authentication](/api/authentication) for how to obtain a token.
+
+## Conventions recap
+
+- Base URL: `https://your-checkmate-host/api/v1`
+- Response envelope: `{ success, msg, data }`
+- IDs: 24-character MongoDB ObjectIds
+- Timestamps: ISO 8601 UTC
+- Durations: integers in milliseconds
+- Most resources are team-scoped — pass `teamId` where the path includes `/team/...`
+
+See [Conventions](/api/conventions) for full details.