In the meantime, I have found a workaround:

I now use this Flutter package, called web_usb

And with some modifications to fit my device (especially concerning the endpoint-addressing), I have a working solution now that fully works also if running in release mode:

flutter run -d chrome --release

As of the other library usb_device I did not understand the described security issue from the answers and how to circumvent it. Maybe you can show a concrete example ?