I don’t really see how the former could work really well in anarchy. Like hypothetically say you “owned” a workshop that could make something useful for the community, they would probably collectively agree that… they should just walk in and start using it. What next?
On the other hand, it seems to me that the general idea of markets could be used. Like, if there was a community workshop, but you were unusually good at making shoes, and had a workstation at that workshop, presumably nothing would prevent you from trading your shoes to other people. The economic value doesn’t really come from the asset of the workstation in that case, though, it comes from your abilities, right?