How to stream PC desktop + phone webcam on Discord?

So here is my goal: stream either gameplay or usual desktop stuff (perhaps CAD designing) alongside bluetooth headset that's connected to my phone, bonus if I can overlay my phone camera as a face overlay.

I can think of a few possible work arounds:

1. OBS desktop and webcam into a virtual camera, using that on Discord desktop.

PROBLEM: No viable headset, as when I use bluetooth headset, it interferes with my mouse that is also BT, and so they both end up freezing out.

2) If there was a way to send my PC screen, to my phone, and use that as my "camera" on discord, that would probably work?

PROBLEM: I don't know how to do that, OBS doesn't seem to interact with mobile.

3) Point the phone camera at my TV/monitor.

PROBLEM: This works, but it's a joke answer. I don't prefer to do this.

\_\_\_

please and thanks in advance!

EDIT: I'm using CachyOS btw and android samsung 🤮 phone