I'm talking about the search engine in question.
The "search engine in question" is using the google api. If the search engine in question serves it means that google actually serves it. Thus I am a bit suspicious of the motivation behind this kind of question; why do you pose it for mullvad and not for any other search engine?
I don't know anything about the subject. But in my mind it kind of made sense that serving illegal stuff is somehow worse if you can't identify the users (eg if police has a warrant) compared to if you can.