The G25 and G27 are not official GT wheels. The Logitech Driving Force Pro and GT are. This is why those wheels are shown on the wheels menu, but the G25/7 aren't, along with tens of other wheels which work with the console but are not official wheels of the game.
The G27 doesn't have a separate sequential/H-gate switch unlike the G25. The fact you didn't know this before laying "300" out on it isn't the fault of the game. The fact Logitech removed this feature from a wheel which isn't officially supported by the game isn't the fault of the game either.