I created a multisorting following the tutorial for spikeinterface 0.90. After creating my multisorting I can extract all spike trains using multisorting.get_all_spike_trains(). But I can't extract it ...

How did you obtain the multisorting object? A simple solution is to cache it first (sorting_cached = se.CacheSortingExtractor(multisorting, "my-path.npz") and then dumping sorting_cached to pickle.