You can use pgTAP for postgres unit testing, with docker you can make the process pretty fast too. Id highly recommend looking into the features/extensions of postgres, there's a lot of great stuff that goes beyond just being a database which can save a lot of time and grief depending on the application.

There is a risk of mixing storage/business logic, and you might end up being tied to postgres, but it's manageable using functions/views/schemas. And its also a really convenient place to do some business logic, as all your data is right there and available via a very expressive/extensible query language.