What is the correct course of action in this situation?

In this situation, a traffic sign indicates that the right-hand lane will end in 200 meters. According to German road rules, when your lane is ending, you should continue in your lane until you are close to the point where it ends—so after about 200 meters, you move to the left. Until that point, you are not required to immediately change lanes.

While still in the right lane, you may overtake vehicles traveling in the lane to your left, because you are not changing lanes yet and overtaking on the right is allowed within marked lanes in built-up areas if lanes are clearly separated and you are not exceeding the speed of the left lane.

You correctly chose to move over after around 200 meters and identified that you are allowed to overtake vehicles on the left under these circumstances. It would not be correct to move immediately into the left lane, as you still have space in your lane and doing so early could disrupt traffic flow. This approach ensures safe and efficient merging and aligns with German driving rules.