I haven't found any new cards from the latest update. Do I need to somehow unlock them first by buying the treasure chests? Or, are they just so rare that I will eventually find some?

Non-basic cards are usually unlock first when you buy treasure chest before you encounter them in-game.

 

Same with some character deck cards and adventure specific cards which are unlock when you purchase that character/adventure.

Yes, new treasure cards must be unlocked by opening treasure chests. Once unlocked, they'll be available for any of your party's to discover while adventuring.