I must correct myself.
There's a silent culprit that wasn't on my radar: the cable.
The so-called “Universal Serial Bus” is anything but universal. Today's USB-C cables and plugs are sometimes used for data, sometimes for high-current charging, sometimes for both. This bus is simply subject to too many specifications that establish the so-called USB "standard".
Knowing this, I had purchased a USB cable that, according to the advertised specification, meets the highest USB standards. Like most of these things it was made in China and apparently this cable is a fake.
Today I tested the connection to the Grenadier again with a different cable and suddenly everything worked like magic.
So if you have similar problems: don't trust your cable.