+1 to sibling comment about not choosing the SOTA just cuz SOTA (if you're in the market for an ANN algo). Almost all the ones there are pretty darn fast these days and many (e.g. hnsw) are implemented out of the box by libraries like nmslib.

Also, most search use cases have requirements besides just the "get_k_nearest" functionality too (scoring-level filtering, business logic built into scoring unrelated to similarity, disparate query patterns that don't fit nicely into a single similarity space), so unless you only need to retrieve the K most-similar documents it might not be a good solution.