[Feature] Add Clear/Reset Button to Search Boxes on Pages Missing It Across Creative Commons Sites

## Problem
On some Creative Commons pages, the search button does not include an option to clear/reset the search box. Two examples are:

[legaldb/cases](https://legaldb.creativecommons.org/cases/) and [legaldb/sholarship](https://legaldb.creativecommons.org/scholarship/).

In other cases, this feature is present, such as on the main page.

[Main page search](https://creativecommons.org/?s)

## Description
Adding a clear/reset button to search boxes across all pages that lack this feature would make it easier for users to reset their search without having to delete text manually. This would improve usability and create consistency across the Creative Commons sites.

The button could appear as an "X" icon inside the search field that clears the search when clicked.

## Alternatives
Keep the current setup: Users manually delete the text in the search field, which is less intuitive and inconsistent with other parts of the site.

## Additional context

This is on main page

This is on legaldb page

## Implementation

- [x] I would be interested in implementing this feature.

Start by comparing the search boxes on legaldb/cases and legaldb/scholarship with the main page search, which already includes the feature. Identify the shared search implementation and check the other pages using it; done means every missing search box has a clear/reset control that works consistently.

Written by the indexing model from the issue text.