I would never expect entropy to stay the same. Technically it could stay the same. But it is unlikely it ever would. What it cannot do - at least not without adding energy to the system - is decrease.You yourself admitted that the SLoT says entropy can increase or STAY THE SAME, so if your last claim were true than entropy could NEVER stay the same. You can't have it both ways, you can't correctly claim entropy can stay the same, and then incorrectly claim that entropy ALWAYS increases.But don't forget that every transfer from energy to matter or matter to energy is not perfect (SLoT). There are no thermodynamic processes that are 100% efficient.
The only time the universe was ever perfectly ordered was prior to expansion and cooling. Ever since that time it has become more and more disordered.