Isn't this what abstraction is? A computer looks magical if you don't understand binary logic gates and transistors etc. Even though I understand it all, the things my computer can do seems magical. I think this is what people mean when they say "emergent" but for some reason don't use more widely understood terms like "high levels of abstraction".
Perhaps this hints at us not even understanding the lower levels of many areas well enough yet.
I expanded my comment because an important thing is to discuss whether the different levels are actually a property of the universe or just a property of our description? Is math discovered or invented. What is part of the map and what of the territory.
I think people use emergence more when it's viewed and suggested as independent from our description, it really emerges on its own and we just discover and describe this. And "abstraction" is used when we view our role greater, we invented an abstraction to easier manage the complexity. So emergence is more incidental, accidental, serendipitous and unexpected, while abstraction is intentional and purposeful and designed.
Now which is which and whether the distinction itself touches on something real or is just a different view of the same thing, is another great topic for discussion.
Perhaps this hints at us not even understanding the lower levels of many areas well enough yet.