feat: frontend auth — login/register modal + user badge

- API service (api.js): fetch wrapper with JWT, auto-refresh on 401
- AuthContext: user state, login/register/logout, loading, roles
- AuthModal: tabbed login/register form matching .pen design
- User badge in toolbar (Sandbox + WorldMap) with initial avatar
- "Entrar" button when not logged in
- CSS: auth overlay, card, tabs, inputs, error state, user badge
- Auth is opt-in: app works fully without login

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

packages/client/src/main.jsx

@@ -2,16 +2,22 @@ import React, { useState } from 'react';
 import { createRoot } from 'react-dom/client';
 import App from './App';
 import GameApp from './game/GameApp.jsx';
+import { AuthProvider } from './services/AuthContext.jsx';
+import AuthModal from './components/AuthModal.jsx';
 import './index.css';
 
 function Root() {
   const [mode, setMode] = useState('game'); // 'game' | 'sandbox'
 
-  if (mode === 'sandbox') {
-    return <App onSwitchToGame={() => setMode('game')} />;
-  }
-
-  return <GameApp onSwitchToSandbox={() => setMode('sandbox')} />;
+  return (
+    <AuthProvider>
+      {mode === 'sandbox'
+        ? <App onSwitchToGame={() => setMode('game')} />
+        : <GameApp onSwitchToSandbox={() => setMode('sandbox')} />
+      }
+      <AuthModal />
+    </AuthProvider>
+  );
 }
 
 createRoot(document.getElementById('root')).render(<Root />);