the "spookiness" only comes into it when you try to understand how this would happen in a classical system.
This isn't a classical system, it's a quantum mechanical system. It's just how quantum mechanics works.
A good analogy is: how do electromagnetic waves travel through a vacuum? If you try to understand "how" from the perspective of someone who only has experience of sound waves which travel mechanically through a medium, the fact that electro magnetic waves travel through a vacuum may appear spooky.
But it's not, that's just what electro magnetic waves do. We can express this behaviour mathematically and predict how electro magnetic waves will behave and then verify those predictions experimentally.
Does this mean we know how they travel? No. We only know that they do. Do we know how quantum entanglement works? No, we only know that it does. We can express the behaviour mathematically and make predictions that are verified experimentally. No more spooky than radio.
QED pop science articles are deliberately confusing people.