Currently, to set up a test site for PostgreSQL development you need to do it manually, and if you encounter any obstacles, you're on your own compared to the number of MySQL developers. In addition, MySQL developers have MediaWiki-Vagrant which ensures that developers have a reproducible environment that is independent of whatever customizations they did to their system.
MediaWiki-Vagrant should offer that functionality for PostgreSQL as well so that MediaWiki developers can easily test features or debug issues caused by different SQL syntax, etc.
There is a broader approach in T73235 for choosing between MySQL and MariaDB, and a similar request for SQLite with T67843, but I think it would be sufficient for the moment to have a vagrant config item db_type defaulting to mysql that, when set to postgres, would instead install a PostgreSQL server and configure MediaWiki accordingly.
AFAICT, the Vagrant configuration is passed to the guest VM as Puppet facts. There are a number of MediaWiki-Vagrant roles that explicitly use resources of the mysql module to set up databases & Co., but these could be extended at a later stage (if they are used outside WMF).