It seems incredibly inefficient if each search actually costs them 1.25 cents. Obviously, I have no real idea, but I just can't imagine that Google earns even a penny per search from ads.
First search result (not a credible one but I can't find a better number) says google does 2 trillion searches per year [0], or at least on that scale. Two trillion at a penny each would be $20 Billion. And you'd expect some economies of scale, though maybe some inefficient in running their ad and tracking apparatus. No idea what google actually spends but their revenue is something like 250 Billion so $20 billion is an underestimate. Anyway, in that context, Kagi's numbers don't sound to weird.
[0] https://searchengineland.com/google-now-handles-2-999-trilli...