How would you differentiate between dragging and rotation?
Quite easily.
One example of the Coriolis effect is things curving as they move along Earth, unless they follow the equator.
Due to the rotation of Earth, things in the northern hemisphere curve to the right. This applies regardless of if they are going north or south or east or west.
Things in the southern hemisphere curve to the left.
If instead this was a result of the heavens rotating and dragging things, everything would curve to west.
If you were to have something go north from the equator, it would curve to the left, towards west. If it went south from the northern circle it would curve to the right, to the west.
See how it is fundamentally different?
But it would also effect things like Foucault's pendulum.
The coriolis effect causing them to rotate, with each path moving slightly to the left or right. This causes the motion to build up and results in a rotation.
If it was drag, it would be pushed to the west, and effectively just look like it was swinging at a slight angle.
If it was swinging east-west, then it would merely shift the centre of the swing slightly to the west.
Reality matches the Coriolis effect, not the heavens dragging things.