Update: somehow I missed the ‘Logic & Behaviour’ tab. I see now that I can set ‘Override the default WordPress search results…’ to Off, so that problem is solved.
I also see that I can set <Return>/Magnifying glass to trigger only Live search. But I still would prefer a simple results list page if possible. BTW “location: Open new tab” does not work, it opens in the same tab and unlike what people are use to from Google, Bing etc. the search box disappears. You have to go back.