Homomorphic encryption reveals less information to the server about the query than if you were to encrypt keys (with deterministic encryption) and values. It hides the fact that the same query was run multiple times and which key (if any) was matched.
I mainly thought it was neat there's a way to do matching on encrypted data without deterministic encryption. It's based on this example - https://github.com/homenc/HElib/tree/master/examples/BGV_cou... - which explains more about how it works and why it's O(N).
The post doesn't say you should give out your login. It says you should encrypt your access tokens and explains some security implications of current implementations that use them, like how they often give too broad permissions. When you change your password, you often need to reauth all of your devices, but you don't need to reauth your access tokens.
Update: Hey ak4g, the latest version of pgslice uses this approach. We're seeing roughly 20% less load on inserts with it (in the short time it's been in production). Thanks for the suggestion!
It uses IVFFlat indexing, but could be extended to support product quantization / ScaNN.