Introduce AuthContext and refactor layout for dependency injection

- Added `AuthContext` as a dependency injection wrapper over the Zustand auth store to support test isolation, E2E testability, and clean architecture patterns.
- Updated `layout.tsx` to utilize `AuthProvider` and initialize authentication context.
- Removed redundant `AuthInitializer` from `providers.tsx`.
- Enhanced modularity and testability by decoupling authentication context from direct store dependency.

frontend/src/lib/stores/index.ts

@@ -2,3 +2,6 @@
 // Examples: authStore, uiStore, etc.
 
 export { useAuthStore, initializeAuth, type User } from './authStore';
+
+// Authentication Context (DI wrapper for auth store)
+export { useAuth, AuthProvider } from '../auth/AuthContext';