The search results page cannot be edited via a plugin unfortunately, it's fully controlled by the actual theme you are using, that's why this is not listed within the features anywhere. Usually the search.php file is responsible for the output (this also depends on the theme structure), which you can find in the currently active theme directory.
I'm working on a possible solution for a future release, sort of a results page builder with a custom shortcode, but that is a very long way from release – due to limitation regarding overriding page contents and differences within themes. It still won't be able to change the layout of the default results page automatically, it's not possible.
This plugin can only override the page layout, but it can override the results (unless there is another override active within the theme). You can read more about that in these chapters:
– Magnifier and Return event redirection
– Results override
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