Phase 1: auth, room CRUD, WebSocket chat, PWA frontend

Invite-only FastAPI + SQLAlchemy(async) + Postgres backend (session-cookie
auth via CLI-provisioned accounts, open-room CRUD, single-instance /ws/chat)
and a React + Vite PWA frontend (login, room list, chat view). Backend tests
pass against a local Postgres DB. See README.md and backend/README.md for
setup, and ARCHITECTURE.md for the full phased design.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/routers/health.py

@@ -0,0 +1,8 @@
+from fastapi import APIRouter
+
+router = APIRouter(tags=["health"])
+
+
+@router.get("/api/health")
+async def health() -> dict[str, str]:
+    return {"status": "ok"}