>> We can predict the behavior of a gyro but there is still a fundamental question of what a gyro is relative to since GR tells us there is no universal reference frame.
If one can see that the gyro is still pointing in the same direction, then one has already defined a reference frame. I can see confusion if we had a gyro spinning inside a free-falling elevator (or even a closed box spinning in space). You can still tell the gyro is spinning because there are internal stresses that indicate the axis of rotation, if not the direction. The earth bulges at the equator because of its rotation, it would require much force to keep it spherical.