Social media platforms play a pivotal role in shaping political discourse, but the scale and rapid evolution of online content make systematic analysis difficult. We introduce an end-to-end framework for inducing an interpretable topic taxonomy from unlabeled text corpora. The framework combines embedding-based clustering with iterative large language model (LLM) inference to construct a topic taxonomy without requiring predefined labels or seed topics. It first synthesizes candidate topics from document clusters and then uses the resulting taxonomy to assign consistent topic labels across clusters. We evaluate the approach through a case study of political advertising ahead of the 2024 U.S. presidential election. We use the induced taxonomy to support downstream analyses of issue prevalence, moral framing, advertising spend, and demographic exposure patterns. These results suggest that iterative taxonomy construction can provide a scalable and interpretable approach to organizing large unlabeled text corpora while supporting substantive downstream analysis.