feat: expose index and chat over FastAPI (Phase 1 Step 5)

[vineethwilson15]

Goal

Create api/ with FastAPI routes mirroring the CLI.

Acceptance Criteria

• POST /index -- runs RepoIndexer, returns stats
• POST /chat -- returns { answer: str }
• GET /health
• No business logic in route handlers -- delegates to core/
• OpenAPI docs at /docs
• Unit tests with mocked core clients