Velocity is the first derivative of position, not the first derivative of distance. Although the distance is constant the position is not.there is (from my perspective, you will surely correct me if I'm wrong) no relative motion between the base station and the rocket. I mean: The distance between them never varies, right? So how can there be a velocity between them?
However, think of the geometry here. In spacetime one path is a straight line and the other is a helix. The relative velocity is the angle between the tangent vectors. The tangent vector to the straight line points along the axis, and the angle of the tangent vector to the helix points diagonally. So the angle between them is not zero, they are not parallel.
I think the geometric approach is best, but what you say here is correct. You have to add the caveat that the formula differs for inertial and non-inertial frames.this might be a new approch for me to grasp the idea of the root cause for both time dilation and ageing differently: May be it is not the relative motion between an observer and an observed object which drives time dilation and accumulated relative ageing but rather the movement path of the observed object through the reference spacetime frame of the observer