feat(chat): ship the grounded chat and retrieval slice

[kpeez]

This PR turns the rebuilt PaperChat app into a real grounded-chat product by adding retrieval, conversation persistence, a first-class chat UI, and the runtime hardening needed to exercise that UI reliably in local browser runs.

Summary

• adds the backend chat/retrieval contract on top of persisted chunks and conversations
• adds the /app/chat experience and promotes the product shell from library-only to library plus chat
• hardens local launch behavior so frontend port drift no longer breaks browser fetches

Why

• PaperChat already launched, ingested PDFs, and managed a local library, but it still stopped short of the core product promise: grounded chat over user-owned papers.
• Live browser testing also exposed a real runtime paper cut in the launcher/dev-origin path that needed to be fixed before this slice could feel stable.

Changes

• add backend chat endpoints, typed chat/citation models, deterministic grounded answer generation, and conversation persistence
• add sqlite-vec retrieval over persisted chunk embeddings and keep the vector index synchronized with chunk lifecycle changes
• wire the chat service into the FastAPI app and allow local dev CORS origins across localhost and 127.0.0.1 ports
• split the frontend shell into /app/library and /app/chat, add shared navigation, and add the chat API client
• ship a transcript-first chat UI with conversation history, source selection, inline source disclosure, and a library-to-chat entrypoint
• require the expected Vite frontend port during launcher startup and keep launcher tests aligned with that stricter contract

Testing

• cd backend && uv run ruff check paperchat tests && uv run ruff format --check paperchat tests && uv run ty check && uv run pytest -q
• cd frontend && pnpm lint && pnpm build
• uv run --group dev ruff check paperchat_cli tests && uv run --group dev ruff format --check paperchat_cli tests && uv run --group dev pytest tests/test_launcher.py -q
• uv run paperchat launch and browser smoke the library-to-chat flow with a ready PDF