I am not familiar with the Hermite interpolator (in general, not just the one from Orekit) and I was wondering what is the recommended usage for orbital data in general and Cartesian states in particular?
I understand that it is a sort of generalization of Lagrange polynomials, with the ability to accurately extract the first derivatives. So I’m guessing there is a risk of Gibbs/Runge phenomenon (I mean oscillations) when there is too many points?
If I’m not wrong, splines (cubic or Akima) automatically create sub-intervals of interpolation, so that such a behavior is less likely with them?

Yes, you can see Hermite as a generalization of Lagrange with derivatives added.
This implies that it uses the same fundamental hypothesis : the built polynomials goes exactly through the data points you give (value and derivatives). This implies that it is also sensitive to small inaccuracies and may also wander far away if the values or derivatives are not exact, like Runge phenomenon.

Splines are a way to limit this. Another way is to use fitting so a small degree polynomials goes close to a large set of data points. In this case, as you have much more points than the degree of the polynomial, you don’t get exactly through the points, but only close to them, but you avoid Runge phenomenon.

Thanks for the insight Luc.
Scipy has got cubic Hermite splines, maybe the best of both worlds?
I noticed they perform better than standard splines near the bounds of the interpolation interval.
As for Akima it seems to require a much denser grid to be a good match.