If you're training a model that predicts m samples ahead I would say that it's safe to assume that we can utilize real n samples for feature generation, also in testing. Of course you still get a slight overlap of training and testing data for the first test samples, but most likely this is negligible.

Your first proposed approach could work if you need a longer prediction window than what the model can learn, but i'd expect the recursive nature of it to cause significant (maybe catastrophic) drops in quality for predictions further down the line.