Did it really sink Reality Winner?
Apparently she was only one of six people who had accessed that particular document, and when questioned she admitted what she'd done. So I doubt those dots had anything to do with fingering her, though that makes a good story as a cautionary tale to other would be leakers.
Seems pretty simple to avoid though - don't give people the actual document you printed on a printer that can be traced back to you. Running it through a scanner at a lower resolution that lose those tiny identifying dots but leave the text and graphics still legible, or if it is 100% text use OCR. If you need paper of some sort print that electronic product on a public printer like at a hotel business center.