Since the transmitter/receiver hooks up via USB, it isn't yet supported by the Stadia controller. They said USB headset support is coming but nobody knows when at this point. You'd be able to use it when playing Stadia on PC and phone, though.
Hi Kenny I'm in a similar situation. This headset will work by plugging straight into the 3.5mm jack. However getting the headset to work wirelessly doesn't work yet. Hopefully this will change. If the Arctis 7 is similar to the Arctis 1, then there is a wireless adapter that hooks up via USB. The sound quality also is extremely low for some reason.