Woohoo! I am now the proud owner of a GraphQL API for my Fly Postgres.
The External Connections was exactly where I needed to go. I first needed to get a dedicated IP address (which makes sense) and then it just worked.
Display Name: [user created tenant label]
Database Name: [not postgres; not repmgr…the other database name in your set of three]
Environment: [doesn’t matter for connecting; this is just some tag to label tenants as dev or prod]
Hostname: [the name of your fly postgres application: [mydatabasename].fly.dev]
I also created a database admin user so as not to use the postgres --connecting my Fly postgres to pgadmin was straightforward (first logged in with default user: postgres and pwd: OPERATOR_PASSWORD and went from there).