feat: implement start page with Create/Join room forms

[Copilot]

This PR implements the start page layout with Create new room and Join by UUID forms, replacing the previous test implementation at the root route (/).

Changes Made

Start Page Component (/src/app/page.tsx)

• Replaced the live text sync test implementation with a proper start page
• Created clean, responsive layout using existing Tailwind CSS styles
• Implemented two main sections: Create Room and Join Room

Create New Room Feature

• Added "Create Room" button that integrates with existing /api/room POST endpoint
• Includes loading state with spinner animation during API call
• Handles API errors gracefully with user-friendly error messages
• Redirects to /room/{roomId} on successful room creation

Join Existing Room Feature

• Added form with UUID input field for joining existing rooms
• Implements client-side UUID format validation using regex pattern
• Shows appropriate error messages for invalid UUIDs or empty input
• Redirects to /room/{roomId} when valid UUID is provided
• Includes loading state during navigation

UI/UX Improvements

• Responsive design that works on mobile and desktop
• Consistent styling with the existing application theme
• Loading spinners for better user feedback
• Clear error messaging for both validation and API failures
• Proper form handling with prevent default and validation

Technical Details

• Uses React hooks (useState) for state management
• Proper TypeScript typing for API responses
• Client-side navigation using window.location.href
• Form validation with regex for UUID v4 format
• Error boundary handling for network failures

The implementation follows the existing code patterns and maintains all build, lint, and test requirements. All 193 existing tests continue to pass.


Fixes #13.

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[Copilot]

Pull Request Overview

This PR transforms the homepage from a live text sync testing interface into a proper start page with room creation and joining functionality. The implementation provides a clean, user-friendly interface for users to either create new rooms or join existing ones by UUID.

• Replaces test implementation with production-ready start page interface
• Implements room creation with API integration and error handling
• Adds UUID-based room joining with client-side validation