Authorship verification (AV) is the task of determining whether two texts were written by the same author and has been studied extensively, predominantly for English data. In contrast, large-scale benchmarks and systematic evaluations for other languages remain scarce. We address this gap by introducing GerAV, a comprehensive benchmark for German AV comprising over 400k labeled text pairs. GerAV is built from Twitter and Reddit data, with the Reddit part further divided into in-domain and cross-domain message-based subsets, as well as a profile-based subset. This design enables controlled analysis of the effects of data source, topical domain, and text length. Using the provided training splits, we conduct a systematic evaluation of strong baselines and state-of-the-art models and find that our best approach, a fine-tuned large language model, outperforms recent baselines by up to 0.09 absolute F1 score and surpasses GPT-5 in a zero-shot setting by 0.08. We further observe a trade-off between specialization and generalization: models trained on specific data types perform best under matching conditions but generalize less well across data regimes, a limitation that can be mitigated by combining training sources. Overall, GerAV provides a challenging and versatile benchmark for advancing research on German and cross-domain AV. Our code and information about data access are available on GitHub.