Fix homepage logo visibility in dark mode

[VPatil3155]

📌 Linked Issue

Closes #395

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📝 Summary of Changes

• Added theme detection using useTheme from next-themes.
• Updated the homepage logo to adapt in dark mode by applying an invert filter.
• Improved logo visibility and contrast while preserving the existing appearance in light mode.

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🔧 Type of Change

• 🐛 Bug fix
• ✨ New feature / enhancement
• 🧹 Refactor / code cleanup
• 📄 Documentation update
• 🧪 Test addition or update
• ⚙️ Configuration / tooling change

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🧪 Testing Steps

1. Installed project dependencies using npm install.
2. Started the application using npm run dev.
3. Verified that the homepage logo is black in Light Mode and changes to white in Dark Mode, improving visibility.

Environment tested on:

• OS: Windows 11
• Browser: Google Chrome
• Node version: v22.x

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🎥 Demo

Attached screenshots demonstrating:

• Light Mode (logo visible in black)
• 
• Dark Mode (logo visible in white)

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✅ Checklist

• My code follows the project's coding style and conventions
• I have tested my changes locally (npm install + npm run dev)
• I have linked the relevant issue above
• I have not introduced any new linting errors or warnings
• I have updated documentation if needed
• My branch is up to date with main

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🌟 GSSoC Declaration

• This PR is submitted under GSSoC 2026
• I have read and followed the Contributing Guidelines
• I have not plagiarised any content
• This is my original work

[VPatil3155]

can you please check it out
if it is good then please do merge this