Not a physicist. It seems you underestimate the time it takes to get to state. The 2nd law of thermodynamics says in a closed system entropy can only increase until a equilibrium where no interaction can happen anymore and entropy stops increasing. It doesn’t say how that state is reached and how long it will take. Keep in mind that an equilibrium doesn’t mean uniformity. When entropy stops increasing that just means the state of the system stops changing.
In our solar system the sun creates the most entropy because of its size and the amount of fusion. But it will take several billion years for it to become a white dwarf and even then it will probably continue sending out light for many billion years.
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