JetSearch with empty input and checked category

script.js

jQuery(document).ready(function( $ ){
	$('.jet-ajax-search__submit').on('click',function(){
		$('.jet-ajax-search__form').submit();	
	})
	$(".jet-ajax-search__submit").on('keyup', function (e) {
    if (e.key === 'Enter' || e.keyCode === 13) {
        $('.jet-ajax-search__form').submit();
    }
});
});

This code will allow you to search through the search button or 'enter' keypress when your search input will be empty
If you want, to get the results filtered by one of this categories https://prnt.sc/G43Ptecv3N1Q , you should create the Custom Query
In my example I want to query with the Product Categories https://prnt.sc/2DdZrQkBbjfB
As I search through the Products, I create the WC Query https://prnt.sc/dv0jZekhmWhL and the main point is create the Tax Query https://prnt.sc/VPSsynjmTzIv with Query Variable https://prnt.sc/4loxTSdQy4Wk jet_ajax_search_categories
It worked for me as I needed https://www.loom.com/share/08d8b9f1beec4be9aef8dfef6b510f26