Issue 12: Deploy frontend (Vercel) + backend (Railway)

[SriMed]

Description

Deploy both services to public URLs for sharing and demo.

Implementation details

• Frontend: connect GitHub repo to Vercel, set NEXT_PUBLIC_API_URL to Railway backend URL
• Backend: Railway with Procfile: poetry run python scripts/bootstrap_data.py && poetry run uvicorn main:app --host 0.0.0.0 --port $PORT
• Add a railway.toml or set the Railway start command to use poetry run — Railway auto-detects pyproject.toml and runs poetry install on deploy
• Set ANTHROPIC_API_KEY as Railway secret env var (never commit it)
• Update CORS to allow Vercel production URL
• Add GET /health endpoint returning {"status": "ok"}
• ChromaDB must be bootstrapped on Railway: add python scripts/bootstrap_data.py && uvicorn main:app --host 0.0.0.0 --port $PORT to Procfile or a Railway build hook
• Update README with live demo URL

Acceptance criteria

• Frontend accessible at public Vercel URL
• Backend accessible at public Railway URL
• 'Load Example' and 'Analyze' work end-to-end in production
• /health returns 200
• ANTHROPIC_API_KEY is a secret, not in repo
• ChromaDB populated on Railway deploy
• README updated with live demo URL

TDD

tests/test_health.py:

1. GET /health returns 200
2. GET /health returns {"status": "ok"}