Yes, multiple moves with the same value are easily found in the opening - trivially from the symmetries on an empty board, and even after a few moves - and in the endgame, where the exact value of moves can be computed and is typically in single-digit points.

In the midgame though, wouldn't it be much more surprising to find two or more moves for one side which have exactly the same value - more than one "best move" - as all the symmetries have pretty much vanished by then ? I'll admit I haven't considered that deeply, just assumed it true.

The superko rule doesn't make much difference to my point above; it is only damaging if there is more than one ko going on, which is relatively rare (but not unheard of). Even in that case it's not the "entire" history of the board which is entangled together, but only a sub-history in which all moves consist of passing or taking back ko points. As soon as you add a stone somewhere (for instance by making a ko threat), superko no longer applies, it's a different position.

If there is only one ko, you only need to include its status in the position's description per AllanCrossman's suggestion below.