well, they are part of the original, canonical problem. it's not the original problem's fault if re-tellers omit key information.

They're not. It says he "opens another door, say No. 3, which has a goat". That could mean he deliberately chose a door with a goat or he chose one by some unstated process and it happened to have a goat by chance. It says he "knows what's behind the doors" but that statement means nothing because it doesn't say how he uses that knowledge, if at all. It's full of language ambiguity.

the assumption is told to you in that the game is expected to continue after monty opens a door. if he could open the prize door, the game would describe what happens when he does that

No. That condition holds in all three of the scenarios that I stated. And yet you have 3 different answers. Switching 2/3 win, 1/2 win, and 0/1 win respectively.

You specifically need information that we haven't been given about the counterfactuals. What might Monty have done in other scenarios that we have not yet observed? We don't know. And we're not actually told. That makes that an implicit assumption that wasn't specified.