Large Language Model (LLM) based conversational systems generate vast interaction logs containing critical diagnostic signals such as failure modes and safety violations. However, the cross-turn dependencies, implicit state, and topic drift inherent to these conversations defeat dense retrieval, whose lone embedding cannot concurrently encode discrete structured constraints (e.g., refusal type) and open-ended semantic content. Our central claim is conceptual: conversational retrieval must span two complementary information planes, structured metadata and semantic content, and these are best reconciled by a unified hybrid representation that jointly supports filtering over structured metadata fields and vector similarity search over unbounded open-ended fields. We instantiate this as the Extract-Annotate-Query (EAQ) framework, which derives a metadata taxonomy, applies LLM-driven annotation, and compiles natural-language queries into hybrid graph operations. On the CDR-Benchmark, EAQ lifts NDCG@10 by 30.8% over the strongest dense baseline, with consistent gains across five analytical categories and two external datasets.