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/database.py

@@ -0,0 +1,13 @@
+from collections.abc import AsyncGenerator
+
+from sqlalchemy.ext.asyncio import AsyncSession, async_sessionmaker, create_async_engine
+
+from app.config import settings
+
+engine = create_async_engine(settings.database_url)
+async_session_factory = async_sessionmaker(engine, expire_on_commit=False)
+
+
+async def get_db() -> AsyncGenerator[AsyncSession, None]:
+    async with async_session_factory() as session:
+        yield session