Replace the existing ComboBoxInputWidget with the new TemplateSearchWidget in TemplateWizard, behind the $wgTemplateDataFavouriteTemplates flag. This is a step in unifying the template search and recall feature in TemplateWizard and VisualEditor.
The new widget should behave in (almost) exactly the same way as the existing template search feature, including the optional dependency on CirrusSearch to improve the search behaviour.