What is the right course of action?

Your answer is correct because, under German traffic rules, when overtaking on the Autobahn, you must complete the entire overtaking maneuver before moving back to a right-hand lane. This means you should fully pass the vehicle or vehicles you are overtaking—in this case, the blue car—before returning to the middle lane. Moving back too early could be dangerous and against traffic regulations.

You should not brake to signal the vehicle behind because sudden speed changes while overtaking can cause accidents, and it is your right to maintain a safe and steady speed until the overtaking is finished. Patience and maintaining your line help ensure safety and comply with the "Rechtsfahrgebot" (keep-right rule). Only after fully passing the slower vehicles should you move over to allow faster traffic behind to continue.