As a player I like to think of sharpness as a measure of the potential consequences of a miscalculation. In a main line dragon, the consequence is often getting checkmated in the near future, so maximally sharp. In a quiet positional struggle, the consequence might be something as minor as the opponent getting a strong knight, or ending up with a weak pawn.

Whereas complexity is a measure of how far ahead I can reasonably expect to calculate. This is something non-players often misunderstand, which is why they like to ask me how many moves ahead I can see. It depends on the position.

And I agree, these concepts are orthogonal. Positions can be sharp, complex, both or neither. A pawn endgame is typically very sharp; the slightest mistake can lead to the opponent queening and checkmating. But it's relativity low in complexity because you can calculate far ahead using ideas like counting, geometric patterns(square of the pawn, zone of the pawn, distant opposition etc) to abstract over long lines of play. On the opposite side, something like a main line closed Ruy Lopez is very complex(every piece still on the board), but not especially sharp(closed position, both kings are safe, it's more of a struggle for slight positional edges).

Something like a king's indian or benoni will be both sharp and complex. Whereas an equal rook endgame is neither(it's quite hard to lose a rook endgame, there always seems to be a way to save a draw).