This is the best information I have:

https://support.searchandfilter.com/forums/topic/how-can-i-search-elemntor-column-while-retaining-the-design-of-that-column/#post-209754

What you want should be possible. But note that the shortcode above the grid, with the filter_next_query in, needs to be a Text Element (using the Text view tab) so that the javascript can be added safely. It cannot be added in the Visual view.