Nope, you didnt miss anything. Larian seems to have missed it. I am playing on PC btw, with a PS4 controller attached, so I get the same nice pretty UI and experience as you are getting on the PS4. And I also do not have a formation button, or any other way to change the formation. I can solve it on PC, by exiting the game, coming back in, and starting with keyboard mode. Once I am in keyboard mode, the entire UI changes to the old-style, including the same party UI with the button on top. But when I come in via controller-mode, the new fancy UI is back and there is no function for party formation.
I really want to see them fix this, because playing with the controller (and getting the updated UI and experience that goes with it) is the BEST way to play this game, by far. Its fabulous!