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
L. Diosan, M. Oltean, A. Rogozan, und J. Pecuchet. GECCO '07: Proceedings of the 9th annual conference on
Genetic and evolutionary computation, 2, Seite 1873--1873. London, ACM Press, (7-11 July 2007)