Remove search form from 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-&gt;formBuilder()-&gt;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.