Is there a way to show everything that was changed in a PostgreSQL database during a transaction?

Dude, What are you looking for is the most searchable thing on the internet when it comes to capturing Database changes. It is a kind of version control we can say.

But as long as I know, sadly there are no in-built approaches are available in PostgreSQL or MySql. But you can overcome it by setting/adding some triggers for your most usable operations.

You can create some backup schemas, and tables to capture your changes that are changed(updated), created, or deleted.

In this way you can achieve what you want. I know this process is fully manual, But really effective.