Page not found: Custom search form with a custom search page

You can use the template_redirect action to add /search/ to your search URL’s. Check out the code below:

function my_change_search_url() {
    if ( is_search() && ! empty( $_GET['s'] ) ) {
        wp_redirect( home_url( '/search/' ) . urlencode( get_query_var( 's' ) ) );
        exit();
    }   
}
add_action( 'template_redirect', 'my_change_search_url' );