If Google specifically denied tracking that’s definitely misleading, but I’m unable to find a source for it and don’t recall it myself.

Saying that the sites you visit track you would absolutely lead me to believe that search engines sites are included. Since it would not be possible to provide results for the search without knowing what was searched for by the user. And where would they send those results to without knowing the users IP or other form of network address? It just doesn’t make any sense to think a search engine would not know who searched for what, since it is required for them to function.