Carry On Together controller support is there and improving — many improvements to controller (gamepad) support are listed among the demo update's new features — but every on-screen control list in the demo is still a keyboard-and-mouse layout.
Carry On Together controller support: what the demo says
Gamepad support exists, and the demo update put a long list of controller improvements at the top of its new features. The wider multiplayer pass in the same series of updates added one-click friend invites, a player list and much clearer voice chat, so the game has been worked on in the areas a gamepad player cares about.
Player reactions are still cautious rather than negative. One demo verdict put it plainly: could be enjoyable with full controller support, definitely has the potential to be fun. Getting the whole crew into one session is a menu away, and the pause menu is where it starts — the invite friends guide covers the invite and the player list.
The control lists you will actually see
Every control list in the demo is a keyboard-and-mouse layout, on foot and behind the wheel alike.
On foot: Left / Right Click - Grab & Carry, E - Interact / Enter Vehicle, Q - Kick, R - Ragdoll, V - Emote (Hold), Ğ - Radar, J - Task Sheet, M - Map, T - Push to Talk (Hold), Middle Click - Ping.
Driving: W / S - Accelerate / Reverse, A / D - Steer, Space - Brake, H - Horn, G - Toggle Headlights, B - Radio (Hold), C - Third-Person Camera, M - Map, F - Exit Vehicle, Middle Click - Ping.
While you are holding something the list grows again, with Mouse Wheel - Rotate Item and G - Drop Equipment added next to Drop - Hold to Throw.
The gap that matters for a gamepad
The mouse wheel is the dedicated Rotate Item binding while carrying, and that is the main reason a gamepad player is missing a control. Everything else in the list maps to a button, but turning a sofa through a doorway needs a wheel, and the rotation itself is only available while several players are holding the piece.
There is a workable answer in the meantime: angle the character rather than the furniture, walk the piece in from a different direction, and use Drop - Hold to Throw when the angle will not work. The two-player carry guide covers the rotation itself and when it appears.
The job sheet guide covers the contract you will be reading with the same keys on either device.