[UI] Fix Navbar to Show User Profile When Signed In

[laurenwu22]

Objective
When a user is signed in, the navbar should display their profile avatar with a dropdown menu. When not signed in, the navbar should show a Login option.

Tasks

• Integrate useSession from next-auth/react into Navbar.tsx
• Conditionally render navbar content based on authentication state:
  • Unauthenticated: show Login link (existing behavior)
  • Authenticated
    • Hide Login link
    • Display the user’s profile image
    • Make the avatar clickable to open a dropdown menu
• Implement dropdown menu actions:
  • Go to Profile → navigates to /user-page
  • Sign out → calls signOut from nextauth
• Ensure behavior works for desktop nav and mobile hamburger menu

Acceptance Criteria

• ✅ Navbar correctly detects authentication state using NextAuth session
• ✅ Logged-out users see a Login link
• ✅ Logged-in users see their profile picture instead of Login
• ✅ Clicking the profile picture opens a menu with:
  • Go to Profile
  • Sign Out
• ✅ Sign out successfully clears the session and updates the navbar
• ✅ Mobile and desktop nav both behave correctly