Is it possible to override/extend existing Popup actions in EXB with custom logic?
For example extending the export functionality to have an 'Export to PDF' functionality with a custom defined PDF template.
Another use case would be adding some custom link on the popup that sends data to another widget.
It seems like the map popup isn't its own widget and therefore not extensible like this.
Take a look at this example for how to build a new action on a popup.
https://developers.arcgis.com/javascript/latest/sample-code/popup-actions/
To make this concept work in Experience Builder, it is possible to write a custom widget with no visible appearance designed to interact with the underlying JavaScript API.