No, it is a myth. The factor of 10 comes from a 2023 calculation that overestimated ChatGPT's consumption at around 3 Wh per query. Current references (Epoch AI, Google's own measurement) put a short query at between 0.24 and 0.3 Wh, and a Google search at between 0.04 and 0.3 Wh depending on the reference point. The real gap is roughly 1.5 to 3 times, never a factor of 10.
Read the source article: ChatGPT vs Google search energy: is it 10 times more?