The Dark Barony's first ability doesn't behave like a leaves-the-battlefield triggered ability, since the card put into a graveyard may come from anywhere. If a card is put into a graveyard from the battlefield, its color is checked in the graveyard, not as it last existed on the battlefield.
The Dark Barony
The controller of a face-up plane card is the player designated as the "planar controller." Normally, the planar controller is whoever the active player is. However, if the current planar controller would leave the game, instead the next player in turn order that wouldn't leave the game becomes the planar controller, then the old planar controller leaves the game. The new planar controller retains that designation until they leave the game or a different player becomes the active player, whichever comes first.
A face-up plane card that's turned face down becomes a new object with no relation to its previous existence. In particular, it loses all counters it may have had.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Pete Venters
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
