Error "Connection timed out. Is the server running ... and accepting TCP/IP connections" Refreshing Postgres Extract

Issue

Postgres Extract fails to refresh in Tableau Online with the following error:
Connection timed out
Is the server running on "server name" (ip address) and accepting TCP/IP connections on port xxxx?
Unable to connect to the server "server name". Check that the server is running and that you have access privileges to the requested database.

Additionally, when trying to connect to the Postgres data source on Tableau Desktop, the following error occurs:
Canceling statement/ terminating connection due to conflict with recovery.
User query might have needed to see row versions that must be removed.
Error fetching next row

Environment

Tableau Online
Tableau Desktop
Postgres

Resolution

Ensure that you are connected to the primary, rather than the standby, Postgres database. For more information, see PostgreSQL ERROR: canceling statement due to conflict with recovery at StackOverflow.