First: make your headset both defaults
Windows keeps two defaults for each direction of sound. The Default Device is what most apps use: games, browsers and music. The Default Communication Device is a second choice that call and chat apps can open instead. When the two point at different headphones or microphones, your game plays in one place and your call in another.
For one headset that does everything, make it both: on the Playback tab of Windows’ Sound window, right-click the headset, choose Set as Default Device, right-click it again and choose Set as Default Communication Device. Do the same for its microphone on the Recording tab.
Open the Sound window
On Windows 11, open Start, Settings, System, Sound, then select More sound settings under Advanced. On Windows 10, the same Sound page has Sound Control Panel under Related settings. The window that opens has the Playback, Recording and Communications tabs.
When you plug in a headset, Windows reads how its maker set it up, and one meant for calls can be given the communication role while your speakers stay the default device. That is why a new USB headset can take over your calls but not your game.
What it means for your stream
OBS captures whatever you choose under Settings, Audio: Desktop Audio for what the computer plays, Mic/Auxiliary Audio for your voice. Choose each device by name there rather than Default, so a change in Windows, or a headset plugged in mid-stream, doesn’t move your stream’s sound.
Your call app has its own device menus too. If guests are missing from the stream, check that the call plays to the device OBS captures; OBS audio routing covers keeping the call, the game and your voice on separate sources.
When your game goes quiet during a call
Windows can mute or lower other sounds while an app uses the communication device. That choice sits on the Communications tab of the same Sound window. Choose Do nothing if your game or music drops in volume whenever a voice chat connects.
Questions
Which should my headset be? Both, if it is the only thing you listen on. Keep them apart only on purpose, for example speakers for the game and a headset for calls.
The headphones are set as default but still silent. Then the role isn’t the problem: follow no sound in your headphones for mute, enhancements and the driver.