feat: add multiplayer memory game functionality with UI improvements

[Chiranthdv]

Description

This PR adds a fully functional Multiplayer Memory Game along with an improved local 2-player Memory Game. The implementation introduces real-time synchronization using Socket.io, enhanced UI styling, correct card-flip behavior, and stable turn-based gameplay.

The feature includes:

• Full multiplayer support (P1 vs P2) with synchronized game state
• Local 2-player mode for offline play
• Accurate player-role loading (P1 or P2) via localStorage
• Real-time turn switching and match updates through WebSocket events
• A UI rendering fix that ensures both flipped cards appear correctly before match checking
• Grid loading fix for Player 2 by triggering state initialization on mount
• Modern UI with Tailwind styling for the grid, cards, scoreboard, and turn highlights
• Smooth animations for flips, matches, and turn transitions
• Winner calculation and display for both game modes

This PR significantly enhances gameplay consistency, ensures correct state synchronization between players, and improves the overall user experience.

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Key Features Added

🎮 Multiplayer Mode (Socket.io)

• Real-time synchronized memory game
• Flip events broadcast to opponent
• Matches update scores live for both players
• Server-managed turn switching
• Full-state sync when a player joins late
• Reset functionality over sockets

👥 Local 2-Player Mode

• Turn-based card flipping
• Accurate mismatch/match handling
• Correct flip timing so the second card always shows
• Independent score tracking
• Clean visual feedback

🎨 UI & UX Improvements

• Tailwind-based polished layout
• Responsive grid size scaling
• Styled scoreboard and turn indicators
• Matched cards highlighted with animations
• Loading state for when Player 2 waits for server sync

🛠️ Fixes Applied

• Second card now always reveals before checking match (timing fix)
• Player 2 grid not showing — fixed by forcing initialization on mount
• Proper role assignment using localStorage
• Consistent flip/match logic across both modes

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Motivation & Context

This feature significantly increases the interactivity and playability of the app by offering both online multiplayer and local two-player gameplay. It also fixes several core visual and logic issues, such as:

• Second card not showing before match evaluation
• Player 2 not receiving initialized board
• Turn desynchronization issues
• UI inconsistencies between different grid sizes

The update creates a stable, enjoyable, and visually appealing memory game experience.

Fixes # (issue)

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Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• UI improvement (non-breaking styling enhancement)
• Breaking change (feature affecting existing functionality)
• Documentation update

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Additional Notes

Future enhancements may include:

• Flip animations using Framer Motion
• Sound effects for matches and flips
• Animated winner screen
• Spectator mode for multiplayer
• Real-time chat inside the game room

This PR lays the foundation for all future multiplayer expansions.

[Chiranthdv]

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