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/routes/auth.routes.ts

@@ -0,0 +1,13 @@
+import { Router } from 'express';
+import * as authController from '../controllers/auth.controller.js';
+import { authenticate } from '../middlewares/auth.middleware.js';
+
+const router = Router();
+
+router.post('/register', authController.register);
+router.post('/login', authController.login);
+router.post('/refresh', authController.refresh);
+router.post('/logout', authController.logout);
+router.get('/me', authenticate, authController.me);
+
+export { router as authRoutes };