The PostGreSQL server operation with Resolve is designed for local area network connections, same subnet, as you need very low latency between the client and the database server. Extremely low.
The DaVinci Resolve Project Server provides a simple interface for the PostGreSQL server to help you manage databases, back them up and share multiple DaVinci Resolve clients. It does not change the fact that low latency is needed between the clients and to the database server.
Numerous test of VPN and dark fibre or raw internet connection to remote sites show only some degree of operation, likely ok if there is only one live user and the DB server is where they are, and the other site is for backup. We cant recommend remote network operation at this time.