Well, that was fun
Unless you are suggesting that the characters are actual sentient entities, it really is the same question.
Or, to put it another way, what’s the practical purpose at the table of saying the character’s “should” know? Not might know, or can know, or probably know....but “should”?
As I asked someone above, do you tell your players who the king is and how the currency works? As opposed to payers who have played D&D before and therefore know about troll fire weakness.
Re. semantics of should, could, might, or can... I misspoke. I meant “flarg’. Which is all of those things. It’s a fun discussion of player v character knowledge, not a boring discussion of the semantics of various words.