Good question. I believe “Print to PDF” isn’t actually “printing” it page by page as if it was a physical printer, but rather just saving the loaded PDF to a PDF file locally.

I’m not an expert in this field, but you can ask on StackExchange, or ask the author of MAT and exiftools, or do it yourself by making a PDF with a jpg file with your metadata, and then extract the image and let us know here - it would be useful information that I can’t find via search engines. I’m using a smartphone so I can’t do it, but if you do, note from the linked SE page is you won’t be able to extract the original file extension, so if you use your own .jpg with your own exif data, rename to .jpg when finished (I believe exif is handled differently based on file type).

There are multiple tools to add exif data to an image but the exiftool website has some good easy examples for our purpose.

exiftool -artist=“Phil Harvey” -copyright=“2011 Phil Harvey” YourFile.jpg

(do this as the first step before adding to the PDF)