I am super ignorant about vector databases, but don't they store n-dimensional vectors, and aren't they used to answer geometric(ish) problems, getting the k closest entries to a particular point?

This sounds a problem more similar to what 3D physics engines can do, but generalized to higher dimensions, as opposed to traditional text and key-based database stuff.

The algorithms and data structures in physics engines (bounding volume hierarchies, kd-trees, etc.) are quite different from how a traditional database index (B-trees and skip lists are popular there, if I remember correctly) is searched and stored.