feat: implement JWT authentication system

Add complete authentication infrastructure including:
- Password hashing utilities with bcrypt
- JWT token generation and verification
- Auth service with register, login, refresh, and logout
- Auth controller with Zod validation
- Auth middleware for route protection
- Auth routes mounted at /api/auth

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

apps/api/src/app.ts

@@ -3,6 +3,7 @@ import cors from 'cors';
 import helmet from 'helmet';
 import { env } from './config/env.js';
 import { errorMiddleware } from './middlewares/error.middleware.js';
+import { authRoutes } from './routes/auth.routes.js';
 
 const app = express();
 
@@ -22,8 +23,8 @@ app.get('/health', (req, res) => {
   res.json({ status: 'ok', timestamp: new Date().toISOString() });
 });
 
-// API Routes (to be added)
-// app.use('/api/auth', authRoutes);
+// API Routes
+app.use('/api/auth', authRoutes);
 
 // Error handling
 app.use(errorMiddleware);