fix(chat): resolve CORS and build issues for local development

- Add webpack builder to nest-cli.json to fix tsc noEmit issue
- Add localhost:5178 to CORS whitelist in backend
- Fix auth token key in api.ts to match @manacore/shared-auth storage

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

apps/chat/apps/backend/nest-cli.json

@@ -5,6 +5,7 @@
 	"compilerOptions": {
 		"deleteOutDir": true,
 		"assets": [],
-		"watchAssets": false
+		"watchAssets": false,
+		"webpack": true
 	}
 }

apps/chat/apps/backend/src/main.ts

@@ -10,6 +10,7 @@ async function bootstrap() {
 		origin: [
 			'http://localhost:3000',
 			'http://localhost:5173',
+			'http://localhost:5178', // Chat web app
 			'http://localhost:8081',
 			'exp://localhost:8081',
 			'http://localhost:3001', // Mana Core Auth

apps/chat/apps/web/src/lib/services/api.ts

@@ -23,9 +23,10 @@ async function fetchApi<T>(
 	const { method = 'GET', body, token } = options;
 
 	// Get token from localStorage if not provided
+	// Token is stored by @manacore/shared-auth under '@auth/appToken'
 	let authToken = token;
 	if (!authToken && browser) {
-		authToken = localStorage.getItem('mana_token') || undefined;
+		authToken = localStorage.getItem('@auth/appToken') || undefined;
 	}
 
 	if (!authToken) {