Is it even possible to breach attorney-client privilege when conducting a plea deal in front of the court?

To illustrate what I mean, I’ll quote an example on the legal TV series “Suits” described by TV Tropes. If it’s inappropriate for this forum, I apologize, I’ll later tell my own interpretation, but I can’t say it any other way.

The description is the following:

Mike Ross faces a dilemma when a client confesses to him that he was stoned when he hit and killed someone with his car. Mike has just secured the client a nice plea bargain on the assumption that the death was purely accidental. Mike’s parents were killed by a drunk driver and his conscience won’t let him keep quiet about what he knows and thus sabotaging the deal, making a weak attempt at hiding how he found out. Katrina realizes that he’s broken confidentiality and chooses to accept the plea bargain anyway, before calling him out on it in private. This one is incidentally okay since a plea bargain is conducted in court: a failure to report the information would violate Mike’s duty of being honest to the tribunal, and would also possibly be suborning perjury (i.e. allowing someone to lie to the court). Of course, Mike isn’t actually a lawyer anyway…

MY INTERPRETATION: I guess what it means is, Mike must violate his attorney-client privilege in front of a judge, and to avoid the court reporter transcribing everything he says, the judge could always let him do it in chambers. Still, he can’t make a plea deal AND not violate his confidentiality at the same time. Still, I’m not an attorney, so I ask you, the experts, to spell it out for me.