feat(web) improve UX with conditional Login/Profile display

[ppcano]

UX: Update header to show "Login" for anonymous users, "Profile" for logged-in users and redirected to main page after logout.

Refactored authentication logic:

• Add shared auth module (pkg/web/src/lib/auth.ts) with:

  • getCookie(): helper to read cookie values
  • hasUserTokenCookie(): check if auth cookie exists
  • verifyUserLoggedIn(): validate session with backend API

• Simplify authentication logic:

  • Remove userTokenStore (was storing random tokens unnecessarily)
  • Add isLoggedInStore to track authentication state globally
  • Use cookie-based auth when logged in, anonymous token for guest access

• Backend: Remove X-Is-Internal header requirement from /api/users/token/authenticate
  endpoint to allow frontend session validation