This is just for data compression, not for computation directly. 32 bits is often overkill for transmission/storage of rotations, unit vectors, geographical locations, unit quaternions, and the like. Depending on the use case 8 bits might be enough, or 12, or 16.

To actually do computation I would convert the posits back into 32-bit floats (or e.g. in the Javascript case, 64-bit floats), and then take the inverse stereographic projection.

[Stereographic projection is extremely cheap; for each data point only requires one division and some additions and multiplications.]

I’ll do some experimenting at some point.