Edit:
That shortcode may need to go to the same area as the search bar is, as live reloading the page may remove it.
If you want to keep filters on that position, the please try this shortcode instead:
[wd_asp id=3]
I have made a search duplicate for you, but that search bar is “hidden away” so only the filters are visible. Because it is separate from the header search, it should very likely work for the live filtering in the original position.