Installing Thrustmaster Warthog Joystick

Hello,
I am trying to install a TM Warthog HOTAS. The throttle device is recognized properly in windows 11, but I'm having trouble with the joystick. Under "devices" in Settings, I can see that the Joystick is recognized as a USB device, but within a few seconds I get a messages "Driver is unavailable". I am not sure what that means; as far as I know I have installed the drivers (and the throttle works fine).
Strangely, in the list of USB devices, the Thrustmaster devices get a new device number everytime I unplug/replug, so e.g. I am now at "HOTAS Joystick Bootloader #8". That seems wrong, too.
Any help greatly appreciated!
Mark

 

The weird thing is that the two devices use the same driver package. Could it be that within that one driver, one device is M1 compatible and the other is not?