Large language models (LLMs) can serve as the semantic-matching engine of a content-based publish/subscribe broker for agentic AI across the edge-cloud computing continuum, bridging the vocabulary and modality gaps that defeat keyword and embedding filters. Framed as offline multi-label retrieval over three public datasets spanning social-media, legal, and smart-home sensor domains (six LLMs, seven baselines), our central contribution is a two-crossover cost-accuracy characterisation: an analytical context-window crossover below which a CoverAndMerge compression pipeline reduces LLM invocations, and an empirical discrimination-capacity crossover above which matching accuracy collapses independently of context budget, by a model-dependent factor of parameter count and training generation. Two findings carry practical weight: above the discrimination crossover, compression cannot recover accuracy and only frontier-scale models clear large subscription sets; and there backend choice dominates configuration choice, so model selection, not pipeline tuning, is the primary operator lever. We accompany this with three composable algorithms and a per-cluster Quality-of-Experience framework for autonomic LLM-tier selection.

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