How should you behave in this situation?

Your choice (answer 1: “Pass through the crossing without stopping”) is correct because the traffic light for your direction is green, and a green light overrides the STOP sign.

In Germany, a STOP sign (and also the stop line/“line of sight” stopping rules) only applies when the intersection is not being controlled by a working traffic light or when the traffic light shows a stop signal for you. If the traffic light is operating normally and shows green, you may drive through without stopping, but you still must proceed with due care: keep your speed appropriate and be ready for possible crossing traffic errors, pedestrians, or cyclists.