I've been researching this topic a bit and it seems like there are few options, but it is definitely possible.
1. Easiest integration, by far, would be to use the Stereolabs ZED, mounted away from the headset instead of on the face of the Oculus.
2. Another option may be the Insta360 Pro/Pro2. Their support has suggested that the video stream would be available through the IP address of the camera on the local network. I have little to no experience with streaming video and the programming required, or streaming video via IP address.
Anybody else know of cameras with this type of capability? Vuze+ VR camera has live stream, but requires internet to stream through an RTMP server.