The output change is in the range of tenths of a percent., maybe closer to around 1 tenth of a percent. The point is it isn't steady, and, as the hydrogen depletes will slowly grow hotter over just a few billion years before it becomes a red giant. At least, that's the current forecast, and no, that's not a joke.
My point in mentioning that is that it's not stable output. Someone with a keen eye might notice a difference in brightness of those old incandescent bulbs as voltage fluctuates within accepted levels. It's a slight change, but still a change. Even a slight change in solar output affects the energy a planet receives from the sun. It may be in the range of tenths of a percent, but it's still a change. It's not equilibrium.