So this was the regional court (Landgericht). The next one is the superior regional court (Oberlandesgericht) where Google will appeal now. Since I don't see any issues of the Bavarian constitution relevant to this case, the next one up is probably the federal court of justice (Bundesgerichtshof). And there is a small chance that either Google or the courts along the way decide to throw this to the EU court of justice.

Most decisions like this get suspended upon appeal, completely or partially, until people give up or there are no more courts to pester. But every appeal will be taken seriously and goes into review at the court whether there is merit to it. That takes time. And Google has the money for a frivolous tour through the courts. And then there is the danger of court ping-pong where the superior court sends this back with notes to the regional. Whose ruling may be appealed again, etc.