Seems like all the recent Death Stranding headlines focused on the special urination mechanic, so I jumped to the wrong conclusion when I saw the new special edition controller.
Here's the official description:
Inspired by the game, this new Limited Edition PS4 Pro features a white matte finish, with two BT handprints that form the shapes of the world’s continents. Sure to bring an otherworldly feel to your home entertainment setup, the bundle also includes an orange translucent DualShock 4 wireless controller that is the same color as the game’s BB Pod. Throughout the game, you can gently rock the controller to emulate holding the BB pod in your own hands.