The balckout was from the brakers at the transformer tripping. From the reports the genrators were still running OK and thus the high voltage supply electricity from which the bow thruster would run still active. The problem with the bow thrusters is more that they are for really low speed, like < 1 knot and they loose effect when going much faster. When they lost power the ship was running at some 8 knots and thus not that slow any-more.
Similar the tug boats would have to litte power to make a real difference at that speed. The habor tugs are made for low speed. So keeping the tugs would also require the ships to go slower.
Such massive vessel could not independently change its trajectory. Even if it is allowed to drift, it will continue to move on the same course. Keep moving in a straight line.
In order for the course to change, it is necessary to apply force. It's just ordinary physics.
The propeller from the main propulsion not only provides the main propulsen, but as an unwanted side effect also a sideways force. When going straight under power the rudder (or a asymmetric hull shape ) has to compensate for this. When the motor (und thus the propeller) stopps, chances are that the propeller slows down the ship a little and produces an opposite side force too.
So the main engine stop not just slows down the ship, but also makes the ship turn. To keep the ship straight after the power loss they need a correction by the rudder.
My point is that this is not a surprising effect and the emergency generator should get steering back fast and powerfull enough to not get such a large excursion from the normal course.
In addition there was also some (though not very strong) wind pushing the vessel to the side it finally went. The the propulsion is lost the rudder gets less effective and thus additional correction needed.
Even in just a "bay" there can be quite some tidal currents. With the shipping channel and relatively shallow otherwise I would not expect the currents to be much sideway though. At least the pilots should have known (such local knowledge is the main reason for habor pilots) and we would have heard about this.