What does Neyman orthogonality protect against?

Let $\psi(W; \theta, \eta)$ be a score function for a target parameter $\theta$ and nuisance parameter $\eta$ . What does Neyman orthogonality at the true nuisance value $\eta_0$ require?

The nuisance parameter must converge at the same $\sqrt{n}$ rate as $\theta$

The score must be statistically independent of every nuisance estimate

The derivative of the expected score with respect to local perturbations of $\eta$ must vanish at $\eta_0$

The Hessian of the empirical loss with respect to $\theta$ and $\eta$ must be block diagonal