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.

.gitignore

@@ -302,6 +302,6 @@ cython_debug/
 #  option (not recommended) you can uncomment the following to ignore the entire idea folder.
 .idea/
 *.iml
-
+.junie/*
 # Docker volumes
 postgres_data*/