...then shuffled that array 115792089237316195423570985008687907853269984665640564039457584007913129639936 (2^256) times uniquely, each time recording the resulting shuffled array.

Correct as an analogy for block ciphers, but note that there are (2^256)! unique permutations of the input space. You're selecting an unimaginably small slice of possible keyed pseudorandom permutations.