Self hosting is a lot more work and you need a separate computer ideally…
To just use zap.stream normally is quite straightforward , download OBS (open broadcast studio).
The hardest part is probably the zap.stream software, just navigating I found hard but if you click on the plus button near your profile pic, then go to dashboard you can find the stream key. That’s what you need to add in OBS, then it should automatically be set up to record from the Mac camera. I don’t know how you’d set up with the phone but I’m sure it’s doable.