I am founder of an entity resolution company. I would not take a vector or graph approach for this (obvious bias, but still we do this day in day out). Vectors are too imprecise for entity resolution, and there is too much risk of entity "leakage" - i.e. over-linking.
Graphs are also not designed for entity resolution and will be slow and run into scaling options.
use a proper entity resolution solution.
There is my company: Tilores Another ER company: Senzing a popular OSS library: Zingg