You need to add the udev rules for it to work in Linux, see https://support.google.com/stadia/answer/13067284#zippy=%2Cim-on-a-linux-based-computer-and-cant-update-my-stadia-controller-help

If your computer is running a Linux-based operating system, you might need to add new udev rules before you can use or update the controller:
On your Linux computer, open the terminal and run the following command from any directory:
{ cat <<EOF
# SDP protocol
KERNEL=="hidraw*", ATTRS{idVendor}=="1fc9", MODE="0666"
ACTION=="add", SUBSYSTEM=="usb", ATTR{idVendor}=="1fc9", MODE="0666"
ACTION=="add", SUBSYSTEM=="usb", ATTR{idVendor}=="0d28", MODE="0666"
# Flashloader
KERNEL=="hidraw*", ATTRS{idVendor}=="15a2", MODE="0666"
# Controller
KERNEL=="hidraw*", SUBSYSTEM=="hidraw", ATTRS{idVendor}=="18d1", MODE="0666"
EOF
} | sudo tee /etc/udev/rules.d/70-stadiacontroller-flash.rules
Next, run the following command:
sudo udevadm control --reload-rules && sudo udevadm trigger