The move from sail boat to power boat can, at first, be "surprising". When we picked up our new to us NT in Anacortes to bring her back to Canada, we had no experience handling a power boat of this size (even though the sailboat was basically the same size). My first docking attempt (at Deer Harbour) was "adventurous" to say the least. Turning radius, getting her alongside were both very different. The slip we were assigned required a sharp turn to starboard, bow in. This would have been very easy with the sailboat.
To me, the biggest things I learned through trial and error, a lesson with a large yacht Captain, and reading, are speed through the water, prop wash and walk, and an almost lack of steerage at slow speeds (in neutral).
We found that to turn in the smallest radius, first stop the boat (or very close to stopped), turn the rudder to the position necessary (usually hard over), and apply forward gear (often only at idle speed). If a sharper turn is needed, apply a very short burst of higher rpm. Forward momentum can be controlled by the duration of the burst (or forward application) and/or applying reverse gear to slow or stop. Sometimes we used a technique we called "ouching" that involved multiple (2 or 3) very short bursts in forward gear (starting from a stopped position) with the rudder hard over (first thing) followed by reverse to control forward motion. These "bursts" can basically "kick" the stern over in the direction of the turn a fair bit without producing much if any forward motion.
Our NT definitely turns more easily (certainly backs and fills) easier to port but it can be done to starboard as well. Our boat had moderate prop walk to starboard...... much more than our saildrive powered sailboat that had almost no prop walk.
Our NT could be backed in a relatively straight line, but it required "adjustments" along the way. EG. use reverse gear to get way on then shift to neutral (it backs straight in neutral which negates prop walk). To compensate for any unwanted sideways drift due to the prop walk (so for us to compensate for stern movement towards the starboard) turn the rudder to starboard and give a short burst in forward to "kick" the stern over to port without slowing reverse way appreciably. This "dance" ( a small "Z" pattern) in and out of reverse and using forward to adjust as needed, continues as long as needed to obtain a more or less straight path in reverse. Obviously the bow thruster can also be used to "steer" the bow where needed.
The main point is take the time to experiment under calm conditions and learn how your boat responds to various inputs. Maybe take a boat handling lesson from a "pro"?