Implement authentication store using Pinia; create auth store with login, logout, and user fetching functionalities.

Update main entry point to reflect new store structure; change import path for auth store.

Add TypeScript support for Vue components; create shims-vue.d.ts for .vue file declarations.

Create Login and Register views with authentication logic; implement user login and registration forms with error handling.

Refactor HomeView to utilize authentication store; display user information and logout functionality based on authentication state.