No, it is not auto trim.
In Normal Flight Control Mode the 777 is trimmed by means of the Stabilizer. That does not move in response to the turn bias system. The 777 has a speed trim system.
If you change the ATTITUDE of the Airbus, it trims for that attitude- THAT is an Autotrim system.
It is not an autotrim system by another name- it is quite simply not an autotrim system.