That worked, thank you so much! Just for my own curiosity, how did you find that out / debug the issue?
With a lot of testing and trying. My first assumption was that something is wrong with the power supply. So I tried a variety of powered and non-powered USB hubs and also different OTG adapters. Nothing worked. Then I got a Raspberry Pi 4 and tested with that - worked immediately without touching any settings. I then read through a lot of posts in the different Raspberry boards. And while I read a lot that the Pi Zero per se is fast enough (confirmed by looking at CPU usage), I read the hint about the USB bandwidth in another context. So I tried settings that might lower the amount of data to be transferred by the capture stick. In the end it turned out (that’s now my understanding - might still be wrong) that a change in resolution is actually passed on to the stick and reduces the captured image before it is actually passed on via USB (in contrast to the image reduction settings in Hyperion that in my understanding rather serve to lower the CPU load.