Hey, I've been trying to get it to work on OBS, without much luck, and I've come to a somewhat important realisation: Not only do you have to screen share, you also have to have your camera actively be used by OBS for the option to pop up in the menu bar. The same goes for Discord (just tested it) although it means the camera feed on discord will just display the presenter overlay icon, while the screen sharing feed shows the correct presenter overlay camera + screen feed.
The best way to do it in my opinion is to setup a screen capture device and a video capture device to the camera you want on OBS, and to start a virtual camera with presenter overlay which you can directly use as a camera on anything you want. It probably saves both bandwidth and UX. (on apps which don't support it directly, like Discord, for example)