Tricky, yes and no, if it is possible in a perfect way.
Well, that is an old problem. It works—kind off—if the objects are in scale and 30meters away, or at least ... well, read on.
The key idea is, that a perfect pano needs to rotate around the lens nodal point. Which is easy to do for a “mono” panorama. If you have a stereo panorama, the problem starts with the distance between the eyes and then that the rotational point of the head is as well not between the eyes, it is way back.
So, if one revolves now the eyes around the spine axis, both eyes describe a circle. But they should both sit exactly with the nodal point on the axis.
A rule of thumb is, that a mm away from the axis is a meter that will not work based on parallax shift. Well, that is given if the nodal point and the point of interest is on one line with the axis, but for stereo it is not. We have even more shift then. So, we need to push all objects more an more away. Another rule of thumb is, that after 30 meters a small change will not really matter anymore for parallax, or the stereo effect.
On top of that comes the whole and too long discussion where to have your convergent point. In cinematography it is mostly done with leading the eye (movement and change) but with a still image that is not possible.
The only way to get around this is to take many images during one rotation of the eye/spine axis rig and stitch them, as the perspective/parallax is like dough, it nearly floats, based on the motion. The more image slices the better, but also extremely done it all blurs into each other.
If you ask for a perfect stereoscopic representation of something, that needs to be AR/VR, where the head-movement creates for this specific field of view and direction a new image-pair. Those image pairs are more and more different the larger the rotational distance and the closer the objects to the viewer are, hence why a static 360º is kind of a compromise and it shows more or less.
Lets pretend for a moment that we have the perfect “view” for the “horizontal” area, how about the pole-caps? We look down to the floor and need left right for the stereo, but what happens when we rotate 180º, we would need a right left view then ;o) Not simple to solve with a still image pair.
Typically the stereo VR works as we have our attention on something in that, but as you ask for precision, well there is some room for tolerance…
All the best