Test the queries your application is making. I wouldn't put much effort into this. You have to trust that other people test their stuff anyway so why make a difference with a database? I'd much rather test that your backups work.

And that can be done by dumping the database (possibly verifying the content of that dump), taking a backup, restoring the backup to a fresh container, then comparing dump of that freshly restored database to the one you took at the start.