feat: Implement initial multiplayer lobby and game room functionality with server-side room management.

docs/development/devlog/2025-12-14-212500_multiplayer_game_plan.md

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+# Work Plan: Real Game & Online Multiplayer
+
+## User Epics
+1. **Lobby System**: Create and join private rooms.
+2. **Game Setup**: Use generated packs to start a game.
+3. **Multiplayer Draft**: Real-time drafting with friends.
+4. **Chat**: In-game communication.
+
+## Tasks
+
+### 1. Backend Implementation (Node.js + Socket.IO)
+- [ ] Create `src/server/managers/RoomManager.ts` to handle room state.
+- [ ] Implement `Room` and `Player` interfaces.
+- [ ] Update `src/server/index.ts` to initialize `RoomManager` and handle socket events:
+    - `create_room`
+    - `join_room`
+    - `leave_room`
+    - `send_message`
+    - `start_game` (placeholder for next phase)
+
+### 2. Frontend Implementation (React)
+- [ ] Create `src/client/src/modules/lobby` directory.
+- [ ] Create `LobbyManager.tsx` (The main view for finding/creating rooms).
+- [ ] Create `GameRoom.tsx` (The specific room view with chat and player list).
+- [ ] Create `socket.ts` service in `src/client/src/services` for client-side socket handling.
+- [ ] Update `App.tsx` to include the "Lobby" tab.
+- [ ] Update `CubeManager.tsx` to add "Create Online Room" button.
+
+### 3. Integration
+- [ ] Ensure created room receives the packs from `CubeManager`.
+- [ ] Verify players can join via Room ID.
+- [ ] Verify chat works.
+
+## Technical Notes
+- Use `socket.io-client` on frontend.
+- Generate Room IDs (short random strings).
+- Manage state synchronization for the room (players list updates).