In this situation, do you have to signal your intention to return to the right lane with a right turn signal?

Yes, returning to the right-hand lane after overtaking is a lane change manoeuvre. According to Art. 22 para. 5 of the Road Traffic Act, the driver of a vehicle is obliged to signal their intention to change lanes in advance and clearly. Activating the right indicator informs other road users, including the driver of the vehicle being overtaken, of your intention and increases safety.