What is the diameter of the Celestial Sphere?
Arbitrarily large, with a minimum size sufficient to account for the unobservable stellar parallax of most stars.
The size of the sphere needs to be large enough that stellar parallax is not discernable to an ordinary observer.
I guess a light year or two would be sufficient.
As an accurate model of the universe this is thoroughly debunked, but it can be useful for such purposes as navigation, etc.