Thanks for your reply wakecarter! Besides movieComponent.play(), movieComponent.reset(), movieComponent.stop(), movieComponent.seek() were recommend, but all result in errors.
(Videos are not played multiple times in Pavlovia)
(Video stimuli not resetting to beginning in online experiment - #10 by Samantha_Gregory)
I removed the code and set the starting time to 1 second. On the smartphone the videos are still freezing, but it works on my laptop with the following twist: At some point the screen starts flickering.
One solution I can try is to split the experiment in two parts, i.e., give the participants a short break.
(Note for completeness: My video files are very small and very short. I have 53 of them and I added them as additional resources using the experiment properties).