You wrote: "Using 256/81 shows that they used the diameter to relate to the circle"

Yes, they used the diameter to find the 'area of a circle'.
I believe problem 50 of the Rhind Mathematical Papyrus READS: A circular field has diameter 9 khet. What is its area?
The written solution says, subtract 1/9 of the diameter, which leaves 8 khet. The area is 8 multiplied by 8, or 64 setat.
It says nothing about 256/81! but does demonstrate the formula of ((8/9)d)^2 for finding the area of a circle. So nothing about pi in any manner shape or form

Surface area of a hemisphere:
Problem #10 Moscow Mathematical Papyrus READS: You are given a basket with a mouth of 4 1/2. What is its surface? Take 1/9 of 9 (since) the basket is half an egg-shell. You get 1. Calculate the remainder which is 8. Calculate 1/9 of 8. You get 2/3 + 1/6 + 1/18. Find the remainder of this 8 after subtracting 2/3 + 1/6 + 1/18. You get 7 + 1/9. Multiply 7 + 1/9 by 4 + 1/2. You get 32. Behold this is its area. You have found it correctly.

Where does this Ancient Egyptian calculation for finding a hemisphere say any thing about the value of 256/81 as the value of pi you have arbitrarily assigned to the Ancient Egyptians?

You wrote: And at the GP pi squared = 9.87654321.

Yet another willfully ignorant mathematically manufactured a myth.

Jacob