Extension property "Screen"

I'm writing an extension that needs a screen name as a property. The control block "open another screen" shows the available screens in the designer.

Is there an option to get a similar behavior in an extension?

No, unfortunately, it is not currently possible for a standard App Inventor extension to have a property that automatically populates a dropdown list of screen names from the user's project.

You could have a look at the sources, see if that helps: