feat: initial elysium idle game prototype

Sets up the full monorepo with pnpm workspaces. Includes shared types
package, Hono API with Discord OAuth/JWT auth, Prisma v6 + MongoDB
Atlas, and React + Vite frontend with game loop, five tabs, and
Discord-linked save/load.

apps/web/src/App.tsx

@@ -0,0 +1,39 @@
+import { useState } from "react";
+import { GameProvider } from "./context/GameContext.js";
+import { GameLayout } from "./components/game/GameLayout.js";
+import { LoginPage } from "./components/game/LoginPage.js";
+
+const handleAuthCallback = (): boolean => {
+  if (window.location.pathname !== "/auth/callback") {
+    return false;
+  }
+
+  const params = new URLSearchParams(window.location.search);
+  const token = params.get("token");
+
+  if (token) {
+    localStorage.setItem("elysium_token", token);
+  }
+
+  window.history.replaceState(null, "", "/");
+  return Boolean(token);
+};
+
+const isAuthenticated = (): boolean => {
+  const fromCallback = handleAuthCallback();
+  return fromCallback || Boolean(localStorage.getItem("elysium_token"));
+};
+
+export const App = (): React.JSX.Element => {
+  const [loggedIn, setLoggedIn] = useState(isAuthenticated);
+
+  if (!loggedIn) {
+    return <LoginPage onLogin={() => { setLoggedIn(true); }} />;
+  }
+
+  return (
+    <GameProvider>
+      <GameLayout />
+    </GameProvider>
+  );
+};