Right, so... There really are many reasons and there's a difference between what Karas is planning and what everyone on his side thinks he's planning.
To sum it up, admitting his knowledge about the black potion will reveal a card they have which is the antidote and his dragon powers, and will also shift the blame from the council to melmont and everyone else and make the opportunity to dig out the council's corruption from the roots almost impossible since they are tied deeply to religious beliefs of the empire and the subjects and people all hold them in high regards. If he killed them all without exposing their corruption then he risks an uprising and outrage from people of the kingdom. If he says he ordered melmont to make him poison he'll have to explain why he asked for it, and the council's defense would be to claim the king's insanity or his plans to poison THEM and make it a reason for a coup which is what they are hoping for. And if he says yea melmont is a traitor and punish him then the blame shifts from council and that brings us back to square one.
What they need is to make the council kill itself from the inside and dig their own grave. Karas's choice to keep them in the library and have Ashler with them holds meaning.
Spoiler!!!!!! But Karas knows exactly what he is currently doing. He is 100% not being played by the council rn and he is not in their grasp and the black potion ingestion isn't what it seems rn.
You'll understand the plot in his mind later on, but the fact remains that the only way to weed out and end the council's influence is to expose them and end any respect the public has for them, and whatever is currently happening is for that goal, and sometimes that necessitates making the enemy think they're winning.

Why is the king taking the black potion again? If tryude can accuse melman of feeding something strange to the king knowing it's the antidote why couldn't the king just say he ordered melman to make it for him?? Why won't he simply refuse to drink the black potion? I don't understand...