feat(docs): add search functionality to docs site

### Feature Description

Hi Team,
Can we have filter/search functionality on left menu may be on top can have on input box and provide filter functionality

### Use Case

Let say I have been landed to the URL - https://material.angular.io/components/table/examples
And I wanted to see the spinner component and I don't have idea where is spinner component and where to scroll the page.
In this case if I could see the search functionality would be very useful for me to search "Spinner" and then I can get the spinner component options.

Hence this additional feature will provide good experience to users. Thanks!!

Start at the documentation site navigation for the table examples URL, https://material.angular.io/components/table/examples, and inspect how the left menu is presented. Determine where search or filtering would fit, then verify that searching for “Spinner” exposes the relevant component options and that the existing navigation remains usable.

Written by the indexing model from the issue text.