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
R. Cañamares, and P. Castells. Proceedings of the 40th International ACM SIGIR Conference on Research and Development in Information Retrieval, ACM, (August 2017)
T. Rezende, and S. Almeida. Workshop of Theses and Dissertations (WTD) in the 29th Conference on Graphics, Patterns and Images (SIBGRAPI'16), São José dos Campos, SP, Brazil, Universidade Federal de São Paulo (UniFeSP), (2016)