I would propose the following, query vector store for 10 closest categories based on a query, feed it to an LLM, in the prompt ask it to produce a single digit 0-9 representing the number of the most appropriate choice. Use plain text prompt, dont inflate token count with JSON. There you go, you just drastically reduced the output pricing.

Additionally you could experiment with a reranker instead of an LLM or after reranking take top-3 results and then feed to LLM as input in order to reduce input token costs.