feat(web): add multiplayer lobby waiting room

- connects WebSocket on mount, sends lobby:join after connection open
- registers handlers for lobby:state, game:question, error messages
- lobby:state updates player list in real time
- game:question navigates to game route (server re-sends via game:ready)
- displays lobby code as copyable button
- host sees Start Game button, disabled until 2+ players connected
- non-host sees waiting message
- cleanup sends lobby:leave and disconnects on unmount
- lobbyIdRef tracks lobby id for reliable cleanup before lobby state arrives

apps/web/src/routes/multiplayer/lobby.$code.tsx

@@ -1,9 +1,159 @@
-import { createFileRoute } from '@tanstack/react-router'
+import { createFileRoute, useNavigate } from "@tanstack/react-router";
+import { useEffect, useState, useCallback } from "react";
+import {
+  useWsClient,
+  useWsConnect,
+  useWsDisconnect,
+} from "../../lib/ws-hooks.js";
+import type { Lobby, WsLobbyState, WsError } from "@lila/shared";
 
-export const Route = createFileRoute('/multiplayer/lobby/$code')({
-  component: RouteComponent,
+const API_URL = (import.meta.env["VITE_API_URL"] as string) || "";
+
+export const Route = createFileRoute("/multiplayer/lobby/$code")({
+  component: LobbyPage,
+});
+
+function LobbyPage() {
+  const { code } = Route.useParams();
+  const { session } = Route.useRouteContext();
+  const currentUserId = session.user.id;
+  const navigate = useNavigate();
+  const client = useWsClient();
+  const connect = useWsConnect();
+  const disconnect = useWsDisconnect();
+
+  const [lobby, setLobby] = useState<Lobby | null>(null);
+  const [error, setError] = useState<string | null>(null);
+  const [isStarting, setIsStarting] = useState(false);
+
+  const handleLobbyState = useCallback((msg: WsLobbyState) => {
+    setLobby(msg.lobby);
+    setError(null);
+  }, []);
+
+  const handleGameQuestion = useCallback(() => {
+    void navigate({ to: "/multiplayer/game/$code", params: { code } });
+  }, [navigate, code]);
+
+  const handleWsError = useCallback((msg: WsError) => {
+    setError(msg.message);
+    setIsStarting(false);
+  }, []);
+
+  useEffect(() => {
+    client.on("lobby:state", handleLobbyState);
+    client.on("game:question", handleGameQuestion);
+    client.on("error", handleWsError);
+
+    void connect(API_URL)
+      .then(() => {
+        client.send({ type: "lobby:join", code });
       })
+      .catch((err) => {
+        console.error("Failed to connect to WebSocket:", err);
+        setError("Could not connect to server. Please try again.");
+      });
 
-function RouteComponent() {
-  return <div>Hello "/multiplayer/lobby/$code"!</div>
+    return () => {
+      client.off("lobby:state", handleLobbyState);
+      client.off("game:question", handleGameQuestion);
+      client.off("error", handleWsError);
+      client.send({ type: "lobby:leave", lobbyId: lobby?.id ?? "" });
+      disconnect();
+    };
+    // Effect runs once on mount. All referenced values are stable:
+    // client/connect/disconnect from context (useCallback), handlers
+    // wrapped in useCallback, code is a URL param. lobbyIdRef is a ref.
+    // eslint-disable-next-line react-hooks/exhaustive-deps
+  }, []);
+
+  const handleStart = useCallback(() => {
+    if (!lobby) return;
+    setIsStarting(true);
+    client.send({ type: "lobby:start", lobbyId: lobby.id });
+  }, [lobby, client]);
+
+  if (!lobby) {
+    return (
+      <div className="min-h-screen bg-linear-to-b from-purple-100 to-pink-50 flex items-center justify-center">
+        <p className="text-purple-400 text-lg font-medium">
+          {error ?? "Connecting..."}
+        </p>
+      </div>
+    );
+  }
+
+  const isHost = lobby.hostUserId === currentUserId;
+  const canStart = isHost && lobby.players.length >= 2 && !isStarting;
+
+  return (
+    <div className="min-h-screen bg-linear-to-b from-purple-100 to-pink-50 flex items-center justify-center p-6">
+      <div className="bg-white rounded-2xl shadow-lg p-8 w-full max-w-md flex flex-col gap-6">
+        {/* Lobby code */}
+        <div className="flex flex-col items-center gap-2">
+          <p className="text-sm text-gray-500">Lobby code</p>
+          <button
+            className="text-4xl font-bold tracking-widest text-purple-800 hover:text-purple-600 cursor-pointer"
+            onClick={() => {
+              void navigator.clipboard.writeText(code);
+            }}
+            title="Click to copy"
+          >
+            {code}
+          </button>
+          <p className="text-xs text-gray-400">Click to copy</p>
+        </div>
+
+        <div className="border-t border-gray-200" />
+
+        {/* Player list */}
+        <div className="flex flex-col gap-2">
+          <h2 className="text-lg font-semibold text-gray-700">
+            Players ({lobby.players.length})
+          </h2>
+          <ul className="flex flex-col gap-1">
+            {lobby.players.map((player) => (
+              <li
+                key={player.userId}
+                className="flex items-center gap-2 text-sm text-gray-700"
+              >
+                <span className="w-2 h-2 rounded-full bg-green-400" />
+                {player.user.name}
+                {player.userId === lobby.hostUserId && (
+                  <span className="text-xs text-purple-500 font-medium">
+                    host
+                  </span>
+                )}
+              </li>
+            ))}
+          </ul>
+        </div>
+
+        {/* Error */}
+        {error && <p className="text-red-500 text-sm text-center">{error}</p>}
+
+        {/* Start button — host only */}
+        {isHost && (
+          <button
+            className="rounded bg-purple-600 px-4 py-2 text-white hover:bg-purple-500 disabled:opacity-50"
+            onClick={handleStart}
+            disabled={!canStart}
+          >
+            {isStarting
+              ? "Starting..."
+              : lobby.players.length < 2
+                ? "Waiting for players..."
+                : "Start Game"}
+          </button>
+        )}
+
+        {/* Non-host waiting message */}
+        {!isHost && (
+          <p className="text-sm text-gray-500 text-center">
+            Waiting for host to start the game...
+          </p>
+        )}
+      </div>
+    </div>
+  );
 }