What is the right course of action now?

Your choice to reduce speed in this situation is correct and important for safety. In German traffic rules, when approaching a construction site or any potential hazard, you must slow down to ensure you have enough time to react to unexpected obstacles, workers, or changes in the road. Maintaining current speed or moving onto the parking strip could be dangerous—moving onto the parking strip is generally not allowed unless signposted, and maintaining speed near construction zones increases the risk of accidents. Therefore, reducing speed helps you drive cautiously and comply with traffic regulations designed to protect all road users.