Nhost Run
You can find details on how to connect to the database from an Nhost Run service here. If you don’t know the password you can set a new password in the dashboard: Project Dashboard -> Settings -> Database
Public Access
For security reasons, by default your database won’t be accessible online. If you need to access it directly from the Internet, first you will need to enable public access (enabling public access will also show the connection details):Project Dashboard -> Settings -> Database

Public access to your database utilizes pgbouncer. As this pooler is shared infrastructure the pooler will still be available even if your database has no public access configured. The pooler will simply not have access to your database.