Make search input more accessible

Search button into search input doesn't have relevant role
Search input doesn't have state. Looks like we need to add [expanded](https://developer.mozilla.org/en-US/docs/Web/Accessibility/ARIA/Attributes/aria-expanded) state

Locate the search input and its associated search button in the TypeScript components and inspect how their accessibility attributes are currently set. Add the relevant role and expanded state described in the issue, then verify that the search control exposes the correct semantics and state to assistive technologies.

Written by the indexing model from the issue text.