I have no sound output in the rift headphone either in home, or in VR games when I set the output device to Rift Headphones or Audio Mirroring. Before I was using my own headphones with the rift and that was working fine but I decided I was going to try the rift headphone for the sake of convenience. I know it's a software issues since I CAN make them them work sometimes by restarting the OVR service and home several times. And also if I set my windows default audio output to the rift headphones and play music for example, the rift headphones works. So, it's definitely not a hardware issue.
Specs: AMD Ryzen 9 5950X, Deepcool Castle EX 360, 32GB Corsair Dominator RGB 3600MHz, Asus ROG Strix X570-E Gaming, Asus ROG Strix 3080ti, Corsair HX1000, Western Digital SN850 M.2 NVMe 2TB, Samgung 850 EVO 500GB & 840 EVO 500GB in raid0, Seagate Ironwolf 10TB, Corsair 4000D Airflow, Acer Predator X34 3440x1440 @ 100Hz, Acer V287K 3840x2160@ 60Hz, Oculus Rift S, Oculus Quest 2 256GB.
Cybers gone man but he does sometimes lurk. You best bet is to make a support ticket with customer service and have them walk you through what they come up with. https://support.oculus.com/