It’s been suggested that I must strengthen my rotator cuffs to achieve this. Is that right?
No. It's a super common misconception that "rounded" shoulders are caused by weak rotator cuffs, but in reality, "rounded" means unwanted shoulder protraction, which the rotator cuffs do not influence at all.
Protraction is caused primarily by the serratus anterior and pectoralis minor, and the opposite movement, retraction, is caused by the trapezius and rhomboids. Whereas the rotator cuffs are only responsible for rotating the arms.
Even then though, strengthening or stretching are unlikely to do anything to change your posture, assuming that you can currently volitionally move your shoulders into the position that you perceive to be "good" posture.
Regardless, what can I do to achieve it?
Consciously maintain the position that you'd like others to perceive as being your normal posture. Accept that it will never become automatic.