Can there really be an objective measurement? You should think first thing data harvesters would implement is a sort of cloak, to erase any traces of what’s going on. Think Dieselgate, but more sophisticated. E.g. phone detects it’s being tested the way you described, or is in the hands of a state attorney or whatever, the recording/ forwarding/ prcoessing of data stops.
These days, the “suggested searches” are ads in the shape of searches of companies or products, many of which nobody ever heard of. Gone are the days of the genuine “other people searched for this.” It was only a matter of time, I guess.