What is the right course of action now?

Your choice to move into the right-hand lane is correct according to German traffic rules. On highways (Autobahns) with multiple lanes, the right lane is primarily for driving, while the middle and left lanes are mainly reserved for overtaking slower vehicles. If you are not actively overtaking, you should keep to the right lane to allow faster traffic to pass on the left. Moving to the right lane when it is free helps maintain smooth traffic flow, prevents unnecessary lane blocking, and complies with the "Rechtsfahrgebot" (drive on the right) rule. Staying in the middle lane without overtaking can be considered improper use of that lane and may lead to other drivers becoming frustrated or attempting risky overtaking maneuvers.