I have had some issues with the flycast domains. They seem to require SSL when connecting to a pg instance, while internal are more flexible. I couldn’t use the connection string since my db client requires all properties separate and operates on default without SSL.
Under the hood the flycast domains for pg are using the same pg_tls service handler people have access to publicly. You can learn more about it (and how to disable tls here: New proxy handler: pg_tls (PostgreSQL sslmode))