Embeddings are good at partitioning document stores at a coarse grained level, and they can be very useful for documents where there's a lot of keyword overlap and the semantic differentiation is distributed. They're definitely not a good primary recall mechanism, and they often don't even fully pull weight for their cost in hybrid setups, so it's worth doing evals for your specific use case.
"12+38" won't embed close to "50", as you said they capture only surface level words ("a lot of keyword overlap") not meaning, it's why for small scale I prefer a folder of files and a coding agent using grep/head/tail/Python one liners.
It altogether depends on the quality and suitability of the provided embedding vector that you provide. Even with a long embedding vector using a recent model, my estimation is that the classification will be better than random but not too accurate. You would typically do better by asking a large model directly for a classification. The good thing is that it is often easy to create a small human labeled dataset and estimate the error confusion matrix via each approach.
Yes, also for semantic indexes, I use one for person/role/org matches. So that CEO == chief executive ~= managing director good when you have grey data and multiple look up data sources that use different terms.
You could assign the cluster based on what the k nearest neighbors are, if there is a clear majority. The quality will depend on the suitability of your embeddings.
