If you synced an image from a Collection in Lightroom-Classic, then the Cloud only has a proxy 'Smart Preview' file. You cannot then Export the 'Original' from Lr-Desktop.
If you are offline and you only have Smart Previews stored locally, again, you cannot export as 'Original'.
Regards. My System: Lr-Classic 12.3 Photoshop 24.5, ACR 15.3.1, Lightroom 6.3.1, Lr-iOS 8.0.8, Bridge 13.0.3, Windows-11.