When you subtract the mean you are changing the angle of the vector.
Example in 2D. x = [0, 1], the angle is at 90 degrees
Subtract the mean of 0.5: y = [-0.5, 0.5], the angle is now 135 degrees.
It’s interesting that the coordinates are correlated quite a bit, but to get a true answer, I would just take the dot product of the unmodified embedding vectors and report out what you see there.