fix(header): resolve layout overflow and improve search bar responsiveness

[Moamal-2000]

Summary

This PR fixes a horizontal scrollbar and layout-breaking issue occurring between 768px and 868px.

Changes:

• Added gap-2 to the header wrapper for consistent spacing.
• Updated the right-side wrapper with flex-auto and justify-end to ensure it correctly occupies available space and aligns to the right.
• Refactored the Search component:
  • Applied max-w-52, min-w-22, and w-full with shrink to allow the bar to resize fluidly.
  • Hidden the "Search..." text on medium screens (hidden lg:block) to save horizontal space, preventing it from pushing other navigation elements.

Related issues

None

Validation

• bun run lint
• bun run format
• bun run build
• bun run build:registry if registry files changed
• Manual verification completed

Checklist

• I kept this PR focused on a single change.
• I performed a self-review before requesting review.
• I updated docs/examples if behavior changed.
• I added screenshots or recordings for visible UI changes.

Notes

The search bar now gracefully transitions from a full-width input style to a more compact icon-focused button as the viewport shrinks, eliminating the need for a horizontal scrollbar.

Visual Changes (Before vs After)

Before	After

[vercel]

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