I'd be careful about how you interpret the AIS data. It's good for giving other vessels a general overview of the traffic around them, which is its primary purpose; but is not designed or intended to be a high resolution and rapidly updating trace of a vessel's movements.
There are many factors which would have influenced the ship's heading after power loss. If the main engine was not powering ahead, the rudder would have quite limited influence on the ship's heading; and if it was powering astern while the ship was moving ahead, possibly no influence on the heading. The rudder is only properly effective when the ship is moving and powering ahead; it effectively redirects the ahead thrust of the propeller. The combination of current in the main channel, current from the side channel, and wind could explain the change in heading. The final stages of the turn could also, possibly, be the starboard bow grounding on the shallower water between the main channel and the bridge pier.
If they did go hard astern when the lights first came back on, that could account for the turn after that moment. This was my initial thought from the large cloud of dense black smoke and heading change, but I'm now more 50:50 on it.
Trying to resolve all of the above into a reliable analysis of the rudder position seems like a very tall order to me.