It sounds like a problem with the macOS shell or permissions, not Spectre failing the export. App Store builds depend on the save dialog to let them write. If the save dialog doesn't show up or closes itself, the export doesn't do anything.
Make sure that Spectre isn't stopped by going to System Settings, then Privacy & Security, then Files and Folders, and finally Full Disk Access. You could also try exporting to the Desktop, which is a very clear place, and see if Finder even asks you. Some people who are using macOS 15 have had this kind of quiet failure when the security prompt goes wrong.
If it still doesn't work, it's probably a bug in Spectre's export path that only happens in the App Store.