Resolve "Implement offline search"

What does this MR do and why?

This MR implements Pagefind UI, replacing Lunr implementation that is currently in gitlab-docs repo. Using Pagefind UI is much faster than the Pagefind API. Prior to implementing using the UI, we implemented the API here. However, there was a lot of performance issues when it came to a short query like "git" which should work without an issue. The UI tackles this performance issue without extra configurations.

Screenshots, screen recordings, or links to review app

These are strongly recommended to assist reviewers and reduce the time to merge your change.

Main page search:

After search:

Mobile search part 1:

Mobile search part 2:

No results found:

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

1. Configure a local GitLab Docs environment: https://gitlab.com/gitlab-org/technical-writing-group/gitlab-docs-hugo/-/blob/main/doc/setup.md.
2. Just need to run make view. No need to run yarn run dev.

Merge request acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this merge request.

Closes #33 (closed)