Add the custom search input partial

[razonyang]

This PR exposes a template (empty by default) for customizing the search input, which will be included if all existing search options were disabled.

The purpose of this PR is that avoid overriding the layouts/partials/search-input.html which will make other search options unusable and hard to maintain on users/clients side.

[deining]

Looks reasonable to me.

[chalin]

• See inline comment.
• Also, this new feature should be mentioned in the docs.

[SayakMukhopadhyay]

I recently raised #2194 which is related. I think I would prefer if there was a guard for the custom search implementation instead of relying on the presence of search-input-custom.html to activate the feature. All search features are activated by guards and I think having a customSearch or custom-search parameter as a guard would be more explicit and transparent.

It will also help downstream users to use the same parameter as a check while implementing other stuff in other layouts. Moreover, as mentioned in the issue, I would prefer to also override the search script in scripts.html using the same guard.

We can include the script in our search-input-custom.html partial but I prefer to include the script in scripts.html to take the benefit of minification and a single script bundle. See the related PR kubernetes/website#49724 for an idea.