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My first thought went to those M-Disk/BDXL bluray disks which supposed to last 1000 years if you believe the claims. So with 100gb per disk you would need atleast 1000 disks. Probably more since the data probably wont perfectly fill out each disk. Writing to optical media is slow and according to the very first searchresult i found it takes upwards of 3hrs to write and verify a single disk. So with a single drive it would take atleast north of 3000 hours if nothing goes wrong. A year has ~8760 hours btw. Oh boi.
But i wouldnt want to rely on a single copy of each disk. If the data is so important i would like to have atleast 10 copies? So the year would probably consist of only maintaining and repairing several burning rigs and going through like ~~35.000~~ edit: 11.000 blurays and then finding spots to safely store them.
But how will they read the data of the disks in the future? Blurays and todays data formats most likely wont exist anymore. So you would need several redundant PCs with bluray drives which hopefully last that long. The HDD/SSD wont last in them. Linux live disks burned on the blurays? On top foolproof documentation how to operate all that ancient shit.
My head hurts
Seems like it would be feasible to purchase a few hundred of those drives and then store them in vacuum sealed containers all over the place.
I believe that worst case after 100 years, the worst that future data restorationists would have to do is replace some rubber belts, Maybe rework a connector or two.
I would hope a team fighting a time war would have some skills here. I don't have to solve that problem.
The discs actually last several hundred years.