I think the search box was always there, but for some reason it seemed that you needed to select a category...
OK, I just looked up their old layout, and they buried the search bar amongst so much crap that it wasn't clear whether it pertained to the ad or the thing above it, or what... if you even noticed it: https://helios-i.mashable.com/imagery/longforms/04ILIeAX3JAF...
Are you saying that's how Yahoo worked? IIRC, that was optional, they always had the search box:
https://web.archive.org/web/19961023235123/http://www10.yaho...