feat: docsearch integration

[ShubhamPalriwala]

What does this PR do?

The CSS isn't well-mixing bec docsearch v3 does not allow custom styles :( so had to do inlining.
Loom Video for the same:
https://www.loom.com/share/77d17bfe20ad4a83998565cdfdaddf58?sid=a13a3078-290c-4a76-afca-cfda1f467b93

Checklist

Required

• Filled out the "How to test" section in this PR
• Read How we Code at Formbricks
• Self-reviewed my own code
• Commented on my code in hard-to-understand bits
• Ran pnpm build
• Checked for warnings, there are none
• Removed all console.logs
• Merged the latest changes from main onto my branch with git pull origin main
• My changes don't cause any responsiveness issues

Appreciated

• If a UI change was made: Added a screen recording or screenshots to this PR
• Updated the Formbricks Docs if changes were necessary

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[github-actions]

Thank you for following the naming conventions for pull request titles! 🙏

[mattinannt]

I'm getting this error on the dev server

[mattinannt]

Please fix the error so we can get this closer to merging 😊

[mattinannt]

@ShubhamPalriwala thanks; looks good :-)