This is a known issue with the Xbox Series X|S and Microsoft is working on a solution.
Using a previous generation Xbox Controller may resolve this issue.
- Known Issue: Some users noticing audio issues when using a wireless headset if they leave their controller go untouched for ~10 seconds.
- Workaround: The proper teams are aware and looking to resolve the issue in a future update but there is no ETA at this time for that fix. The issue will stop when the user starts to use the controller again or by continually using the thumbsticks/buttons. Alternately, you can also temporarily resolve this by using an Xbox One generation controller.