Comment by uncircle
Your question fascinated me. Googling "where did the Sun got its low entropy" I also came across these explanations:
"Solar energy at Earth is low-entropy because all of it comes from a region of the sky with a diameter of half a degree of arc."
also, from another reply:
"Sunlight is low entropy because the sun is very hot. Entropy is essentially a measure of how spread out energy is. If you consider two systems with the same amount of thermal energy, then the one where that energy is more concentrated (low entropy) will be hotter."
https://physics.stackexchange.com/questions/796434/why-does-...
Probably it's a bit of both. I'm not sure I understand your hypothesis about the Sun scooping up empty, low-entropy space. Wasn't it formed from dusts and gases created by previous stellar explosions, i.e. the polar opposite of low entropy?
The universe was low entropy at the time of the big bang, and even though entropy is steadily rising, the universe is still pretty low entropy.