"How exactly could they get convicted if they haven't lost immunity yet?"

I was referring to the immunity from civil suit. I don't believe a prosecutor is immune from criminal prosecution for a crime committed in the course of a prosecution.

For instance, if a prosecutor tells a defendant, after a trial has started, "Confess and switch your plea to guilty, or I'll murder your family," he would not be immune against prosecution for extortion. (He's getting something of value -- a guilty plea in a difficult case, thus improving his performance stats -- by making a threat.)