Thank you for trying this.

the information on the grid is not enough to draw a symmetry conclusion (without solving more cells)

That's good to know. If the given placement were also symmetrical it would be possible to know from the very start, but I was wondering if it has to be that way.

I will try to find one with symmetrical pairs but not symmetrical placement on the givens that has a non-symmetrical solution (proof by contradiction).

Either way it was based on the fact that all the solved 4s and 6s seemed to have rotational pairwise symmetry, as well as 5s and 7s, and 2s with themselves.

That's just part of the symmetry:

- Rotational symmetry with pairs 22, 13, 46, 57, 89.

But that is just the result of the two main symmetries on the grid combined:

- Diagonal symmetry [ / ] with pairs 22, 44, 66 (inside the diagonal) and pairs 13, 59, 78 (outside the diagonal)

- Diagonal symmetry [ \ ] with pairs 11, 22, 33 (inside the diagonal) and pairs 46, 58, 79 (outside the diagonal)