This just seems like a donation with complicated extra steps, in the same way that e.g. "rounding up to charity" or even "round up savings" do not appeal to me at all.

That might well be an idiosyncratic preference, and to some the idea of "planting trees via running web searches" might appeal much more than a nonprofit search engine that donates to a basket of charities, or one that directly pays the user for showing them ads and lets them decide what to do with the money and then the user donating the proceeds themselves.