feat: improve navbar responsiveness across all device sizes

[Pranav-IIITM]

Description

Improves navbar responsiveness across all device sizes. Updated internal navigation links in the mobile menu to use Next.js <Link> component instead of raw <a> tags, fixing ESLint (@next/next/no-html-link-for-pages) errors and ensuring correct client-side routing. The navbar now adapts cleanly across desktop, tablet, and mobile (down to 320px width) with proper spacing, alignment, and no overflow issues.

PR Summary

• Added a responsive Header component at Header.tsx
• Replaced the old inline header in layout.tsx with the new component
• Added a mobile hamburger menu button (aria-label="Toggle menu") visible on small screens and hidden on md+
• Hid nav links on mobile and kept them available in a mobile drawer, while preserving desktop layout
• Used Tailwind responsive classes only (px-4, sm:px-6, md:hidden, etc.)
• Updated page.tsx so the "⭐ Star on GitHub" button only appears on md+ screens to avoid overlap
• Ensured no new dependencies, no component rewrites beyond the header refactor, and no raw CSS was added

This improves navbar responsiveness from 320px upward while keeping the existing design intact.

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Related Issue

Closes #1295

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Type of Contribution

• Bug fix
• New feature
• Documentation update
• Refactor
• GSSoC contribution

Participant Info

• GitHub username: @Pranav-IIITM
• Contribution level (Beginner/Intermediate/Advanced): Intermediate

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Screen Recording

Recording.2026-05-27.232641.1.mp4

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Checklist

• I have read the contribution guidelines
• My changes follow the project structure
• I have tested my changes in Chrome, Firefox, and Safari
• bun run lint passes (no ESLint errors)
• bunx tsc --noEmit passes (no TypeScript errors)
• New interactive elements have aria-label / accessible names
• No console.log statements left in
• This PR is related to a valid issue
• Screen recording attached above (required for UI/feature/design changes)

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[github-actions]

👋 Thanks for your PR, @Pranav-IIITM!

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🟠 GSSoC'26 PR detected — thanks for contributing under GirlScript Summer of Code 2026!

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Quick checklist

• PR title follows Conventional Commits (e.g. feat: add dark mode)
• Linked the issue this PR closes (e.g. Closes #123)
• Tested the changes locally (bun run dev)
• Build passes (bun run build)

Useful links

• 📖 CONTRIBUTING.md
• 🐛 Open Issues
• ⭐ Star the repo to support the project!

Happy coding! 🎉

[Pranav-IIITM]

@magic-peach Please review the PR