feat: update AuthButton and Header for improved user experience

- Increased avatar and icon sizes in `AuthButton` for better visibility.
- Integrated session handling in `Header` to display user profile link and sign-out button when authenticated, enhancing mobile menu functionality.
- Refactored mobile menu overlay to a modal for improved usability.

src/components/AuthButton.tsx

@@ -41,10 +41,10 @@ export function AuthButton() {
           <img 
             src={session.user.avatar} 
             alt="Avatar" 
-            className="w-4 h-4 rounded-full object-cover"
+            className="w-10 h-10 rounded-full object-cover"
           />
         ) : (
-          <svg className="w-4 h-4" fill="none" stroke="currentColor" viewBox="0 0 24 24">
+          <svg className="w-6 h-6" fill="none" stroke="currentColor" viewBox="0 0 24 24">
             <path strokeLinecap="round" strokeLinejoin="round" strokeWidth={2} d="M16 7a4 4 0 11-8 0 4 4 0 018 0zM12 14a7 7 0 00-7 7h14a7 7 0 00-7-7z" />
           </svg>
         )}