For paid software with which I have no affiliation beyond being a happy customer, there’s Reincubate Camo: https://reincubate.com/camo/

I've been using this method with pretty good result: https://github.com/apancik/iphone-as-a-webcam

Thank you very much, this is exactly the satisfactory solution I haven't found when I was looking for it before! I expected that the iPhones screen recording was only available in Quicktime and not for third-party apps like OBS. Going to try it out soon with an old iPhone 5, I hope it supports streaming video from the camera in the browser.

Doesn’t work with FaceTime, unfortunately.