Assuming that there are no other planets or other gravitational sources around the observer in empty space, would the observer's very fast circular motion create GR gravitational or else called acceleration time dilation?

I am not interested on the SR or else called kinetic constant velocity time dilation, only for the acceleration time dilation? Even if the angular velocity is kept constant, since this is a circular motion the velocity vector direction is changing all the time and therefore must be considered as an accelerated motion. Right? So therefore there must be also a GR gravitational time dilation component together with the SR kinetic time dilation due to the constant angular velocity of this assumed circular motion.

The only reason I could think of for no gravitational time dilation to exist is because the observer's stable path circular motion and angular velocity, the centripetal cancels out with the centrifugal and therefore there is no gravitational time dilation component.

The reason why I am asking this question is because I was puzzled lately by the fact that by the recent g-2 Fermilab muons experiment lecture, in the experiment's muon storage ring (i.e. cyclotron) the only time dilation present they have announced was about (64-2.2)=61.8μs and was purely a SR kinetic time dilation. They never said anything about any GR acceleration time dilation effect due the circular motion, present on the experiment?