If it is not immediately obvious to you how negligible the cost is going to be, you have no clue how little compute small models like this require. Apply a bit of common sense: this is a model designed to run locally on smartphones. If it used a lot of power, the phone would run out of battery.

It's hard (if not impossible) to find power usage figures for Gemini Nano, because they're going to depend on the efficiency of the device it's running on. If it's on a phone (where most Chrome installs are), that phone likely has an NPU, in which case the power draw will be negligible. If it has to run on the CPU, it'll be more.

So let's instead assume every user will be using a model comparable to ChatGPT, for which we do have reasonable estimates. According to this estimate, 500 output tokens would use about 0.3 Wh of energy. 500 output tokens is about 400 words, which is probably more than the average user will be using Gemini Nano for (it is intended for small tasks), but let's assume that as the average daily use. 1 billion users times 0.3 Wh is 300 MWh. Fuck all on a global scale, about 0.0015% of the world's energy production (20 TWh per day).

Keep in mind that figure is for the full ChatGPT, which runs on 1500-watt GPUs. Gemini Nano runs on chips that draw more like 1.5 W, and on devices that physically cannot draw more than 15 W. It's thus reasonable to estimate that it is on the order of 100x more efficient.