Docs: API — publish interactive API docs to a public URL

**Description:**
Swagger is only available locally. External developers need access to API docs.

**Tasks:**
- Export `openapi.json` during the build step
- Host Swagger UI as a static site on GitHub Pages or Vercel
- Add a link to the hosted docs in `README.md`
- Add API versioning prefix (`/v1/`) to all routes
- Document authentication flow with examples in Swagger

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