If you want to utilize a theme search box (such as found in most theme headers and/or main menus) using a WordPress rewrite is best. For this you should be using a child theme (really easy to set up if you don’t know how, using a free plugin from Orbisius – you can delete that plugin once it is done), and you edit the functions.php file and add some code to pass the search terms to our form on the results page. You will want to use code like that shown in this post (change the slug name though to match that of your site search page):
https://support.searchandfilter.com/forums/topic/using-default-wp-search-bar-to-show-sf-results-page/#post-243811
The Search and Filter form must also have a search box in it to ‘accept’ the search terms. I would ‘hide’ (using custom CSS) the header search box on the results page, as otherwise that will conflict with our form if used on that page. If necessary, show me the page when done and I can give you that CSS.
As to working with Elementor Pro, you need an additional extension plugin from us – the link is at the top of this guide (which you need to read and follow):
https://searchandfilter.com/documentation/3rd-party/elementor/
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