To do the home page search just create a rebuilder shortcode and select the redirect page where you want to readirect when submit the search.
after creating the shortcode as usual paste the shortocde in the homepage and in the frontend create your search bar using drag and resize as you want.
then the important part is take a apply filter button in your search block then from the settings panel of apply filter select your search page and redirect option. that's it.
Also you have to make sure you have already setup the the search page where you are redirecting your visitor (the search page you have selected in the apply filter button you have to setup another reactive builder shortcode in that page with same post type and taxonomies so that it can find the result properly. Make sure you don't use same shortcode for your home page and Redirected page.