In short: the issue in my case was the lambda sensor from the exhaust mid section (not the one closer to the engine!).
The symptoms were a front-back jerking at 1900-2100 RPM in 3rd gear when gently accelerating. It occurred in other gears as well but this was most noticeable as I spend quite a bit of time at that exact RPM in traffic.
The code for the actual sensor was not constant in the OBD reader, but the code for the lambda sensor heater was a constant fault code. I ignored it because it wasn't that important but it turned out the whole sensor was bad.
According to my mechanic which identified and fixed the issue, this sensor controls a flap in the exhaust which can cause issues like rocking, poor fuel economy and even exhaust smell in the car if exhaust gasses are forced through other holes in the exhaust when it's damaged.
Replacing the sensor made the car much smoother across the board.