A very common workflow is to index some data based on its embeddings and then given a new query embedding retrieve the most similar examples with k-Nearest Neighbor search. For example, you can imagine embedding a large collection of papers by their abstracts and then given a new paper of interest retrieve the most similar papers to it.
TLDR in my experience it ~always works better to use an SVM instead of kNN, if you can afford the slight computational hit
P. Pantel, and D. Lin. Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining, page 613--619. New York, NY, USA, ACM, (2002)