feat: stats + chat + frontend pages (Stats, Chat, NavBar)

Backend:
- StatsManager.js: JSON persistence, leaderboard, rate-limit 1/5s
- ChatManager.js: 200-msg buffer, JSON persistence
- index.js: routes GET/POST /stats, /chat/history, /chat/send (Zod validation)
- ArenaRoom.js: chat handler broadcasts to room + persists via ChatManager

Unity:
- StatsTracker.cs: distance, maxSpeed, jumps, bumps, checkpoints, raceTime tracking
- ChatUI.cs: F3 toggle, bottom-right panel, polling 3s, unread badge
- NetworkManager.cs: SendChatMessage() + OnMessage<ChatUI.ChatMessage>(chat)
- CheckpointSystem.cs: RegisterCheckpoint/Finish hooks
- PlayerController.cs: RegisterJump/Bump hooks, physics rebalance, billboard fix
- GameHUD.cs: LocalRaceTimer, SetTotalRounds, OnRoundStart signature fix
- GameManager.cs: spectator cam reconnect fix

Frontend:
- NavBar.jsx: fixed top nav, Accueil/Stats/Chat/Jouer
- App.jsx: page state (home/play/stats/chat) + NavBar
- StatsPage.jsx: 6-tab leaderboard, auto-refresh 30s
- ChatPage.jsx: polling 3s, localStorage name, Enter to send

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

rolld_backend/game/src/index.js

@@ -2,28 +2,98 @@ const cors = require('cors');
 const { Server } = require('@colyseus/core');
 const { WebSocketTransport } = require('@colyseus/ws-transport');
 const { ArenaRoom } = require('./rooms/ArenaRoom');
+const Stats = require('./stats/StatsManager');
+const Chat = require('./chat/ChatManager');
+const { z } = require('zod');
 
 const PORT = process.env.PORT || 2567;
 
-// Colyseus 0.17 – express callback receives the transport's internal Express app
+const statsUpdateSchema = z.object({
+  name: z.string().min(1).max(32),
+  stats: z.object({
+    totalDistance:    z.number().optional(),
+    totalJumps:       z.number().optional(),
+    maxSpeed:         z.number().optional(),
+    bestRaceTime:     z.number().optional(),
+    racesPlayed:      z.number().optional(),
+    qualifications:   z.number().optional(),
+    eliminations:     z.number().optional(),
+    checkpointsTotal: z.number().optional(),
+    bumpsGiven:       z.number().optional(),
+    totalPlaytime:    z.number().optional(),
+  }),
+});
+
+const chatSendSchema = z.object({
+  name: z.string().min(1).max(32),
+  text: z.string().min(1).max(200),
+});
+
+let _gameServer;
+
 const gameServer = new Server({
   transport: new WebSocketTransport(),
   express: (app) => {
     app.use(cors());
+    app.use(require('express').json());
 
     app.get('/health', (_req, res) => {
       res.json({ service: 'game', status: 'ok', timestamp: new Date().toISOString() });
     });
 
-    app.get('/', (_req, res) => {
-      res.send('🎮 Game server running');
+    app.get('/', (_req, res) => res.send('🎮 Game server running'));
+
+    // ── Stats ────────────────────────────────────────────────────────────
+    app.get('/stats', (_req, res) => {
+      res.json(Stats.getAll());
+    });
+
+    app.get('/stats/leaderboard/:key', (req, res) => {
+      const board = Stats.getLeaderboard(req.params.key);
+      if (!board) return res.status(400).json({ error: 'invalid key' });
+      res.json(board);
+    });
+
+    app.post('/stats/update', (req, res) => {
+      const parsed = statsUpdateSchema.safeParse(req.body);
+      if (!parsed.success) return res.status(400).json({ error: parsed.error.issues });
+      const ok = Stats.update(parsed.data.name, parsed.data.stats);
+      res.json({ ok });
+    });
+
+    // ── Chat ─────────────────────────────────────────────────────────────
+    app.get('/chat/history', (req, res) => {
+      res.json(Chat.getHistory(req.query.since));
+    });
+
+    app.post('/chat/send', (req, res) => {
+      const parsed = chatSendSchema.safeParse(req.body);
+      if (!parsed.success) return res.status(400).json({ error: parsed.error.issues });
+      const msg = Chat.push(parsed.data.name, parsed.data.text);
+      if (!msg) return res.status(429).json({ error: 'empty or invalid message' });
+
+      // Broadcast to all active Colyseus rooms
+      if (_gameServer) {
+        try {
+          const rooms = _gameServer.matchMaker?.rooms;
+          if (rooms) {
+            for (const room of rooms.values()) {
+              room.broadcast('chat', msg);
+            }
+          }
+        } catch (_) {}
+      }
+
+      res.json(msg);
     });
   },
 });
 
-// Define rooms
-gameServer.define('arena', ArenaRoom);
-console.log('✅ ArenaRoom registered');
+_gameServer = gameServer;
+
+gameServer.define('arena', ArenaRoom).then(() => {
+  console.log('✅ ArenaRoom registered');
+});
 
 gameServer.listen(PORT).then(() => {
   console.log(`🎮 Game server running on ws://localhost:${PORT}`);