Currently if I change the $filename value in a Export config used by an Action, the change fails to take effect on Action "Export file name" until I e.g. enter the Action definition and change the config selection to another, and then back.
Yes, once the report filename has been hardcoded by $filename() in the export script and the script has been saved, then the preset filename in the file selection dialog should be automatically updated to the hardcoded filename ... or ... the file selection dialog should be disabled (greyed out) for such an export script.
I now see the same problem affects the Export dialog from the File, Export command (see edit to root post). There, fixing by disabling would be inappropriate. Also, disabling would obstruct the user making a deliberate manual override. So I prefer your first fix suggestion - automatic update.
I now think this is a bug, so have reported it in Bugs, here /t/16111/1 .