What is the right course of action?

Your answer is correct because, according to German traffic rules, when overtaking a slower vehicle, you should continue and complete the overtaking maneuver promptly and smoothly. Quickly finishing the overtaking maneuver helps prevent obstructing traffic behind you and reduces the time spent in the left lane, which is primarily intended for overtaking. Stopping the overtaking or braking unnecessarily while passing can create dangerous situations and disrupt traffic flow. After completing the overtaking, you should return to the right lane as soon as it is safe. This approach ensures safety and respects the "keep right" rule (Rechtsfahrgebot), which is temporarily relaxed during overtaking.