My response to your other story includes a link to the money-fuel tree. This is where proof-of-work currency fits, it seems to me.
Distributed currency production, at point of distributed energy collection, interchangeable with distributed hydrogen production, and even distributed food production.
https://eric-bott.medium.com/the-fuel-tree-5ef66be03c4
notice how well the integrated hydrogen electrolysis process of fuel production above fits with this:
All are valuable interchangeable product, which should be reflected by the issue of money (Austrian economics ideal)