You could probably implement Solid with Nostr, but I don't think they are inherently similar.

The flaw with this is that if an application can access data from your "data wallet" that is effectively a copy, you're ultimately trusting their data storage/caching policy, so not sure what it achieves. What constitutes authoritative is subjective in the wild, something like that would probably only be applicable in a large network with sub-networks, like the Feds mandating it for states, but then what's the difference between the protocol and a distributed FedDB?