I've found out stone paper is actually UV printable and some small company already offers it in rolls for labels material https://www.lightninglabels.com/biostone-labels

Stone paper is naturally waterproof and photodegrade with 14-18 months of sunlight exposure.

Here some additional technical info: https://www.stone-paper.com/en/stone-paper-the-environment-friendly/

There are some criticism on this material because it's 80% stone powder and 20% HDPE (they call it organic plastic, but it's not specified if it's actually biodegradable and where it goes when the stone photodegrades).

https://www.wired.com/2013/02/stone-paper-notebook/ however, it can be an interesting alternative between paper and vinyl for labels.