What do you mean "search history turned off"?
I'm not sure I understand.
Also, I'm not a UI/UX expert, but Google suite has "Account Settings" where I would have expected to be able to see/change my address, but the option is not there. I use a limited subset of Google products (GMail, Calendar, Youtube, Google Docs, Maps etc...) but the possibility of changing the address was in the only product I haven't used since 2014 (I checked it because someone else, on a forum, pointed me to it).
Now the address is updated, but I have no idea to check if my Data Controller will remain the same or it will be Google LLC.
They should give us an explicit option to check/set what Data Controller we have, not infer it from a single product (which in my case wasn't used anymore).