Finally the third USB video grabber arrived. This time I ordered a Gembird UVG-002 with a UTV007 chipset. I plugged it in, booted the PI and started a SSH session. The command lsusb showed me what I wanted to see…
The grabber was recognized as a Fushicai USBTV007 video grabber… Yeah!
So now I could configure Hyperion to use the grabber and see if I can take a screenshot. It worked… So now everything is working like it should. Project closed.