Adjust the results quantity for Search Results page pagination

Perhaps this function will help you out.
Add to functions.php after you made a backup of this file.

There is no need to add any in a template by using this function.

/**
 * Set max output results for search page
 * 
 * @param  $queryVars
 * @return results
 *
 * Read more   @link   https://developer.wordpress.org/reference/classes/requests   /request/
 * Tested with @version 5.3.2
 * 
 */
add_filter( 'request', 'search_results_pro_page' );
function search_results_pro_page( $queryVars )
{
    // Prevent access to back-end
    if ( is_admin() ) {
        return;
    }

    // Set only on search
    if ( isset( $_REQUEST['s'] ) ) {        
        // Adjust number of results shown
        $queryVars['posts_per_page'] = 4;  
    }
    // Return amount search results 
    return $queryVars;                      
}