OBS can present its output as a virtual webcam, so can Logitech's webcam software, so can driver-level code, so can lots of other things (https://duckduckgo.com/?q=%22virtual+webcam%22, or just search for your own phrase [fake webcam device]). Virtual microphones are similar, and there are lots of options, e.g. Equalizer APO does audio processing in the Windows kernel before applications get it, and supports VST plugins that can generate audio. Browsers see these things exactly how they see hardware webcams and microphones (since those go through drivers in the same way). Chromium or Firefox could easily be modified to have virtual mic and webcam support built-in, without needing driver-level shenanigans. Bots can be run in virtual machines where the "hardware" is just software that can be fed any input you like. Hardware-wise, a Teensy or Arduino can plug into a USB port, pretend to be any USB device, and feed in anything you like. You could even use a computer's real microphone and webcam, just pointing at the speakers and screen of another (but there's not much point, since doing it in software is simpler).

Metadata is trivial to modify, e.g. FFMpeg can do it, and it usually doesn't say anything about genuine-ness anyway. Besides, if you're generating your fake input in software, you'd just generate metadata to go with it.

Sorry, but there are so many holes in your idea that it seems completely unworkable. Even if new developments made it more feasible (new webcams and microphones that cryptographically sign their recordings? Still fakeable by the speakers and screen setup above. Depth-sensing cameras might be trickier.) people would rebel against allowing any and every site to access their webcam and microphone (and hence possibly spy on them).