testing(`node_types`): lightclient integration tests

Light clients (all 3 implementations) have zero unit-test coverage, and are only incidentally covered by the system test in the repo.

This is probably due to the setup difficulty: It requires running a prover for the setup, and this prover+da instance would ideally be shared between the tests. It would be amazing to have some fixture system set up, but I'm not sure at the moment how that should be set up.