Definitely use as much of or as far left in the outside shared lane (don't call it a 'car lane', it is not only for cars) as you need to be safe to avoid being squeezed or closed passed in that lane. Driving far right in the shared lane (such as along the bike lane stripe) may be worse as other drivers will still try to pass and pass you closely. Being so close or partly in the bike lane as they approach from distance they may think of you as out of their way until they are too close to merge left.

The law you noted was about adjacent paths. The bike lane is part of the roadway, not an adjacent path.

Don't compromise your safety whether it is doors that may open, potholes or unpredictable/ambiguous position that will result in close passes.

If you use a mirror you can merge right if and when there are no other safety issues for a long stretch ahead to let faster vehicles pass. Be sure to leave enough time/space to merge back predictably well before any potential hazards.