And so the Sun is not also subject to entropy....?
The whole universe is subject to entropy not just a supposed debatable “closed/not closed system”.
Everything is subject to entropy. But before it disappears, gravity can cause some of the everything to clump together and squeeze down so tightly that fusion results. Energy from the fusion bathes the earth as an outside source of energy. The earth is then no longer in a closed system as long as the sun shines.