My hard copy birth certificate isn’t doing too well even after much shorter time.

If that PDF represents a part of a curated collection, then I’d be willing to bet the data will be readable in a perfectly preserved way in a thousand years. I have been casually copying files and have nearly accidentally preserved all sorts of data that would have been tossed out decades ago if it were paper based.

The key word is curated, and applies to both paper and digital works. If neglected, either one has a risk of being lost or destroyed.

We have survivorship bias about paper records. We see a famous preserved work from a thousand years ago and declare “wow, paper lasts forever, but I lost a burned cd from not even 20 years ago, paper is obviously better”. However that paper was ordered by royalty of the day and put under the curation of a Treasury as a highly valuable artifact from the moment it was created.

Far more paper records have been lost or destroyed than we even know to have existed.