Audio streaming through the Razer Raiju Tournament Edition | RZ06-02610 only works when the controller is in wired mode and connected to the PS4/PC through USB. Connect to the PS4/PC using the included micro-USB cable.
If you're connected to a PS4, hold the PS button to go to Quick Menu, then ensure that the volume control for headphones is not muted, and output to Headphones is set correctly.