feat(api): add WebSocket foundation and multiplayer game store
- Add ws/ directory: server setup, auth, router, connections map
- WebSocket auth rejects upgrade with 401 if no Better Auth session
- Router parses WsClientMessageSchema, dispatches to handlers,
two-layer error handling (AppError -> WsErrorSchema, unknown -> 500)
- connections.ts: in-memory Map<lobbyId, Map<userId, WebSocket>>
with addConnection, removeConnection, broadcastToLobby
- LobbyGameStore interface + InMemoryLobbyGameStore implementation
following existing GameSessionStore pattern
- multiplayerGameService: generateMultiplayerQuestions() decoupled
from single-player flow, hardcoded defaults en->it nouns easy 3 rounds
- handleLobbyJoin and handleLobbyLeave implemented
- WsErrorSchema added to shared schemas
- server.ts switched to createServer + setupWebSocket
745c5c4e3a