My Clubsport had a touch of torque steer when accelerating hard on cambered roads but my R definitely doesn’t seem to.
What tyre pressures are you running?
The steering moving by itself is likely the VDM as fredgroves suggests. There were a few sections of road that would make my Clubsport twitch even at well under 30mph when the radar and whatever system the car uses to anticipate bends or roundabouts detected something it wasn’t happy with. One particular bend was a 90° left hander with a sudden dip, directly ahead where it bends is a main line railway track and the other side of that is sea water (well, estuary water which may or may not be salty) with yachts bobbing about. The car really didn’t like the immediate approach to that bend, if the car was a cat it would have had major tail bushing going on. Any other car I’ve been in just went round it normally.
Other than that both my mk8’s seem to have very stable and predictable steering, in fact I’d list it as one of the car’s best features.
Was your old 7.5 GTI nitrous powered by any chance adekil? 😁