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/ws/connection_manager.py

@@ -0,0 +1,31 @@
+import uuid
+from collections import defaultdict
+
+from fastapi import WebSocket
+
+
+class ConnectionManager:
+    """In-memory, single-process WebSocket registry.
+
+    Correct for a single app-server instance only; cross-instance fan-out via
+    Redis pub/sub is a later phase (ARCHITECTURE.md phase 5).
+    """
+
+    def __init__(self) -> None:
+        self._rooms: dict[uuid.UUID, set[WebSocket]] = defaultdict(set)
+
+    def join(self, room_id: uuid.UUID, websocket: WebSocket) -> None:
+        self._rooms[room_id].add(websocket)
+
+    def leave(self, room_id: uuid.UUID, websocket: WebSocket) -> None:
+        self._rooms[room_id].discard(websocket)
+        if not self._rooms[room_id]:
+            del self._rooms[room_id]
+
+    def leave_all(self, websocket: WebSocket) -> None:
+        for room_id in list(self._rooms.keys()):
+            self.leave(room_id, websocket)
+
+    async def broadcast(self, room_id: uuid.UUID, payload: dict) -> None:
+        for websocket in list(self._rooms.get(room_id, ())):
+            await websocket.send_json(payload)