As someone running neo4j in production I can just warn that the DBs are a pain and need a lot more care and love than Postgres or Oracle DBs. Even much larger instances. Maybe their cloud offerings are better, but they are quite expensive.
Yes, Postgres is actually a great general-purpose graph database (excluding specialized network analysis that's actually pretty niche) if you can deal with the clunky recursive-CTE syntax for graph queries. (The new SQL standard actually comes with an added Property Graph Query/PGQ syntax specifically to make these queries easier to express.)
