Search box component

Textboxes (`mode='text'`) don't support `live=True`.

A textbox with search/autocomplete built in would be useful. Needs to be hooked up to a search term handler. Needs design.

Start by locating the textbox component and the handling for mode='text' and live=True. Clarify the search-box design and the search-term handler contract before choosing an implementation path. Done means a textbox supports search/autocomplete behavior and passes search terms to the agreed handler.

Written by the indexing model from the issue text.