Earlier quoted context omitted.
"How do you save a search in a non-personally identifiable way?" To a first approximation, you just... do it. Granted, if you search "{jerf's realname here} {embarrassing disease} cure" or something, in the pathological case, you could at least guess that maybe it was me, though even then my real name is far from unique, and nothing stops anyone else from running such a search. But otherwise, if all you have is a pil…
At the very least your example is PII which you cannot save and also claim to be Private.
A search history can reveal many things about a person. The mere fact that someone, somewhere searched for "star wars harry potter crossover slash", unconnected to any other search item, doesn't reveal anything about anybody.