Hi,
WordPress does not work like that. The results page is handled by the theme, and by default the plugin redirects there – the plugin cannot replace that, it is not possible. If you have the results page on a custom URL scheme, you can change the search to redirect to that as well.
If you are using Elementor, it is possible to use a custom page as the search results page, you can see it in action here: https://ajaxsearchpro.com/elementor-custom-results-page/