How much does Germany follow case law? If this could set a precedent, it's worth noting that anyone can generate these AI overview responses and they're wrong like 9 times out of 10 only.
In Germany, you also have the Oberlandesgericht and the Bundesgerichtshof as a higher venue for civil cases (and the Constitutional Court as well). So, this is not like "the law has changed" at all. (I'm not a German qualified lawyer, but qualified in a close enough continental system, and on my way to be qualified in a common law jurisdiction soon, that's why I dare to comment on this aspect)
But if you as a first party are publishing something directly, like Google is here, you're generally liable for what it says.
https://www.startribune.com/google-ai-overview-lawsuit-defam...
Previous cases in this space (eg Meta v KGM, Walters v OpenAI) have not turned on Section 230 specifically.