On your listings page, the search bar shows a compact Start your search pill instead of the full bar with date fields and a Search button.
Why this happens. The search bar switches to its compact phone layout when the column it sits in is too narrow to display all fields. On a listings page with the map enabled, the results column defaults to 55% of the page content width. On sites with a content area of around 1100px or less, that is too narrow.
What you can do. Lower the map’s share of the layout in the explorer widget settings under Map settings, using the Map/grid width split option. For example, setting the map to 25% at 960 to 1199px, 30% at 1200 to 1599px, and 30% at 1600px and up gives the results column enough room to render the full bar at desktop sizes, with the Search button and the Where, When, Who, and Filters fields.
The compact pill layout on phones is intentional.