Hi!
Thank you very much for all the details, it helps a lot.
The duplication is due to the fact, that there is second search bar rendered on the page – within a hidden widget. I can see it on the debug console, but it is not visible. It might be either a container for Elementor of some sort. If it is not possible to remove, then using this custom CSS will resolve the issue:
#wpdreams_asp_results_2>div:last-child {
display: none !important;
}