You could try using sys-usb and passing your USB controllers/Bluetooth devices there instead of sys-net.
First, remove them from sys-net if they are present (in the Devices tab of sys-net settings, only keep your network controller). Then, you will be able to run the following in dom0:
sudo qubesctl state.sls qvm.usb-keyboard
It will create sys-usb (if not there already) and the necessary policy rules.
Once it’s finished, you should be able to connect your keyboard in sys-usb via terminal. If all goes well, it will be recognized as an input device, and events will be sent to dom0 to work with all qubes.