Why is distance considered such an important part of what makes quantum entanglement strange?

From what I understand, if two particles are entangled, then when I measure the spin of one, the other one will have the opposite spin. People always emphasize that this still works even if the particles are extremely far apart, like on opposite sides of the universe. But I don’t really see why the distance itself is the strange part.

To me, the actually weird part seems to be how the two particles are entangled in the first place and what that really means physically, not the fact that they can be far apart. Distance doesn’t seem to play an active role here.

It feels similar to having two devices that can show red or blue, where they’re set up so that whenever one shows blue, the other one shows red. If I put one device on Earth and the other a billion light years away, then when I look at the one on Earth and see blue, I instantly know the other one must be showing red. The separation between them doesn’t seem to make that any more mysterious.

So with entangled particles, if I measure one here and get spin up, I immediately know the other one is spin down, no matter how far away it is. That just feels like correlation.

Am I basically thinking about this the right way, where the real mystery is the nature of entanglement itself rather than the distance, or am I still missing something important?