Is there a way, in theory, to export private key from the bitcoin address (watch-only) that is now expired, but used once before? (even to get a different format of that key, numeric one instead of QR code used in the first place?). If everything is traceable, out of curiosity - has anyone ever managed to actually do this?
It is not possible to compute the private key for an address, ever, unless there are severe bugs in the wallet that holds the key.
Also addresses don't expire. For privacy reasons it is bad to reuse them, but their security does not depend on this.
In addition the "now showing as watch-only" in your question seems confused. Addresses don't become watch-only by being used; if it's watch-only it's because it has always been watch-only.