Exporting private key from expired bitcoin address (now showing as watch-only)
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.