Great question, and good to see computers, etc. making it into PB manuscripts, because they are such an intrinsic part of most children's worlds these days IMHO. I have been shopping a ms too that is not about tech, but which incorporates it (no takers so far, but lots of positive feedback). I don't know the answer to your question (is there a definitive one?) but for me, I would either say "searched on line" or merely "searched", with the "on line" part being shown in the illustration (i.e., laptop, tablet, or phone appearing in pic).
Best of luck.