Yesterday, I worked in a support case that our customer needs to review the connection and if possible the execution time spent for Azure Database for PostgreSQL using PGBouncer and not.
I developed and upload a new option in our AzureSQLConnectivityChecker for PostgreSQL in our GitHub project, in order to review this connection time spent for the application. You need to install ODBC and create the DSN first.
In this same resource our AzureSQLConnectivityChecker you could find the same connection checker for Azure Database for MySQL, Azure Database for PostGreSQL, Azure SQL Database, Azure SQL Managed Instance and SQL Server OnPremise. I have done all these tests working with customer cases with very good results.
I will be more than happy if you could collaborate adding more options in these PowerShell scripts.