The short version is: yes, it wants to turn because the thrust comes from the far side, but planes also have very big rudders in the tails. Adjust it a few degrees to the side to compensate and the plane can fly straight and turn both ways. You can “trim” it, permanently setting the “center” position as said few degrees to the side.
That said, planes will usually need to reduce speed and descend from their ideal cruising altitude since they’ve lost some power and that rudder to the side is going to cause a decent amount of drag.
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