Migration has been a core topic in German political debate, from millions of expellees post World War II over labor migration to refugee movements in the recent past. Studying political speech regarding such wide-ranging phenomena in depth traditionally required extensive manual annotations, limiting the scope of analysis to small subsets of the data. Large language models (LLMs) have the potential to partially automate even complex annotation tasks. We provide an extensive evaluation of a multiple LLMs in annotating (anti-)solidarity subtypes in German parliamentary debates compared to a large set of thousands of human reference annotations (gathered over a year). We evaluate the influence of model size, prompting differences, fine-tuning, historical versus contemporary data; and we investigate systematic errors. Beyond methodological evaluation, we also interpret the resulting annotations from a social science lense, gaining deeper insight into (anti-)solidarity trends towards migrants in the German post-World War II period and recent past. Our data reveals a high degree of migrant-directed solidarity in the postwar period, as well as a strong trend towards anti-solidarity in the German parliament since 2015, motivating further research. These findings highlight the promise of LLMs for political text analysis and the importance of migration debates in Germany, where demographic decline and labor shortages coexist with rising polarization.