But I think that I have a half-duplex communication here because at the device, I only have three outputs : A, B and GND
Both half-duplex and full-duplex are only with the two wires A / B and GND. The difference is that the half duplex interface only either can send or receive data, and which one it does is controlled by an extra signal on the UART side, usually DTR. The full duplex interface has extra logic to detect when the TX pin is idle and then automatically switches over to receive mode. Whenever the TX pin goes active it will switch back to sending.
Full duplex is simpler to implement on the UART side since you don't have to control the extra DTR pin at all. But it can be difficult to get to work with some devices when their timing is critical and you use a high Baudrate such as 1MBaud