Bran knows, well, pretty much everything, and his visions of the past, including a key scene in the Tower of Joy, point him to the truth about Jon Snow's parents. Later, after learning about Sam's research, Bran goes and sees the wedding of Rhaegar Targaryen and Lyanna Stark, confirming what they believe to be true.
TBD on whether he'll make it through the Battle of Winterfell, particularly since, you know, he's the Night King's number-one target. If he dies, though, there are still plenty of players who know about Jon Snow's secret.