They're not contracts in the sense of a cryptocurrency, they're contracts in the sense that code and cryptography are used to control how data is used and updated in the system, similar to a database ACL, or object encapsulation in OOP.
This is a generalization of a concept called "signed subspace keys" in the original Freenet, which predated Bitcoin by almost a decade.
> The P2P aspect looks much better, but naturally there's the question of how this is differentiated from something like Tor with .Onion sites?
.Onion sites and services are still centralized, their server's location is just hidden by Tor. With the new Freenet the services themselves are entirely decentralized and can operate entirely independently of the person or people that created them.