The way wordpress works is the reason why the native search results handling is required for the results page. The results page handler is the core wordpress feature where the search results are handled, so the search plugins know where to initiate the search override functions.
For a simpler solution, you can try using Elementor to add a posts archive widget to the results page, but coding it might be just as simple.
The coding should not be any difficult either, all themes come with a results page handler. You can take a sample from the core wordpress themes, the search.php file usually contains the header, footer, the body part, and a simple posts loop:
while ( have_posts() ) : the_post();
/**
* Run the loop for the search to output the results.
* If you want to overload this in a child theme then include a file
* called content-search.php and that will be used instead.
*/
get_template_part( 'template-parts/content', 'search' );
// End the loop.
endwhile;