Facebook share button issue: "Attachment not found: The attachment could not be found."

Same here.

I think it's FB bug (OR they purposely disabled attachment/link sharing for certain accounts).

There was a major outage recently in FB messenger as well: https://developers.facebook.com/status/dashboard/

This is a new bug/development. I had share buttons sharing to FB PM's perfectly fine until about the same time as you posted this.