Hi Daniel,
The problem is, that the search shortcode output is altered by a different script. The navigation buttons are wrapped around paragraph elements, so the event handler is not attached properly. I also see line breaks injected after each element.
If you use page builder elements/widgets, then try a different type that you are using currently. If there is any option on the widget settings that adds ‘paragraphs’ or ‘line breaks’ automatically, then make sure to dislalbe those options as well. Usually text type widgets do that, they are not suitable for HTML content.