For a point of comparison, a ChatGPT request uses 2.9 watt-hours (and rising) to a google searches 0.3 (which per your example would only be run once assuming you’re checking different blogs from the same list of results.)
generally I end up checking some results and often changing the search with new keywords but all the same I generally am doing follow up questions similarly. Im betting to any energy the ai uses to check web destinations is likely not included which would be the same as I going to a destination. maybe less if its more of a crawl or api. Any way you slice it its going to be more I think.