Issue 2: Implement Authentication Flow

## Overview
Complete the authentication implementation using Clerk.dev integration.

## Tasks
- [ ] Test Clerk authentication setup
- [ ] Implement protected routes
- [ ] Add user profile management
- [ ] Handle authentication state changes
- [ ] Add sign-out functionality
- [ ] Test authentication flow end-to-end
- [ ] Add loading states for authentication
- [ ] Handle authentication errors gracefully

## Acceptance Criteria
- [ ] Users can sign in with GitHub/email
- [ ] Protected routes redirect unauthenticated users
- [ ] User profile information is displayed
- [ ] Sign-out works correctly
- [ ] Authentication state persists across page reloads
- [ ] Error handling for failed authentication

## Technical Details
- Use existing `ClerkProvider` setup
- Implement proper route protection
- Add user context management
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