Studies on grandmaster chess players indicate that at most you burn 10% more calories when engaged in deep thought than when you're at rest. So the energy "attributable" to an hour of knowledge work is like 10 calories (average sedentary calorie burn is like 80-100 per hour; add a max of 10% for the thinking gets you 8-10 calories). A pound of potatoes is like a buck and is about 320 calories. So you're looking at like 3 cents an hour at most to cover that energy burn. It's definitely even less; I certainly don't think as hard as a grandmaster chess player.

Then, assume power costs 20 cents per kilowatt hour (US avwrage) To match the human 3 cents per hour, you need an average of 150 watts of power drawn per hour. That's in the range of a budget graphics card, but not much past there.

However, if you sleep instead of sitting around, you can probably make AI cost competitive. Sleeping drops your metabolic rate by more, and lying down in bed (as opposed to sitting) also reduces calorie burn. Combined, you can reduce your burn by like 30 calories an hour. At the new 9 cents per hour human cost, you can afford to run a higher end graphics card at ~450 watts per hour. That puts you in RTX 3090 range.