Rework the search scripts to make it closer to docsy

[SayakMukhopadhyay]

This is a small change towards getting the search functionality closer to Docsy. Its related to #47975 but takes a different approach to the same end. The changes made are as follows:

1. The content from static/js/search.js and assets/js/search.js moved to assets/js/k8s-search.js. This helps with modification and prevents the need to override search,js from docsy/assets/js. The file is also named k8s-search.js in the same vein as Docsy has offline-search.js. This helps in indicating that their functionality are similar.
2. This new file k8s-search.js is incorporated layouts/partials/scripts.html Docsy add all search scripts like the offline-search.js in this file. This addition is also done inside a .Site.Params.k8s_search guard in the same vein that Docsy uses .Site.Params.offlineSearch guard.
   As an aside, I was thinking of seeing if a "custom search" feature could be added in Docsy which would mean that we would just need to add a script and be done with any custom search functionality.
3. The linking of the deleted /static/js/search,js is removed from layouts/_default/search.html

I also plan to rework search-input.html and associated scss files but probably in a different PR.

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[sftim]

As an aside, I was thinking of seeing if a "custom search" feature could be added in Docsy which would mean that we would just need to add a script and be done with any custom search functionality.

Suggest opening an upstream issue about the possibility.

[SayakMukhopadhyay]

Suggest opening an upstream issue about the possibility.

google/docsy#2194 has been created. I will also note the same in the comments to ensure we don't forget to incorporate it if Docsy takes in the change.

[sftim]

Could we adopt google/docsy#1512 anyway, and use that behind the templates.Exists guard (disabling built-in search mechanisms and using our own complicated "you might be subject to state-level censorship" search functionality)?