to be fair, I don't know EdgeDB's architecture but to the degree that a system can bring its graph structures into memory, using PostgreSQL as the durable storage but not for every on-demand query, it can certainly provide fast results. I would assume EdgeDB likely has concepts like this integrated into its design.
a graph database is not useful because of its query language, it's useful because of its performance characteristics when bringing linked data — it could never be performant on a Postgres backend.