What's the best way to remove the search form from the search result page in Drupal 8?
There is not much you can customize in core search. So you probably need to override Drupal\search\Controller\SearchController::view and remove this line:
$build['search_form'] = $this->formBuilder()->getForm(SearchPageForm::class, $entity);
Put your extended class into the route
search.view_node_search in a RouteSubscriber.
But I don't think it's worth the effort. You can either simply hide the form in CSS or if you want a fully customizable search solution use Search API.