What is the maximum speed a vehicle may drive in a zone with this sign?

Your answer “30 km/h” is correct.

In Germany, a “Zone” sign does not just apply to the next junction or the next few meters; it defines rules for the whole area until an “end of zone” sign appears. If it is a 30-zone, then 30 km/h is the maximum speed everywhere inside that zone, even after intersections, unless another sign changes it.

The extra plate “Anlieger frei” means through traffic is not allowed: only residents, visitors, deliveries, and anyone with a legitimate destination inside the zone may enter. It does not change the speed limit; it only restricts who may use the streets.

Rule of thumb for similar questions: In a zone, the speed limit stays the same throughout the zone and continues past crossroads until the zone ends.