Yours might be one of those questions best suited for official Apple Support. The reason is that it would be helpful to allow Apple to remotely examine your Mac (with your permission of course) so that they can see what you are doing and determine where the roadblock may be.
In the meantime please review the following Apple Support document, which may explain things better than I can:
Control access to the camera on Mac - Apple Support
"In Safari, to allow a website to use the camera, choose Safari > Settings, click Websites, then select Camera."
That's pretty much all I can suggest, and if it's not working as it describes then I'm out of ideas.
To contact Apple, start here: Contact - Official Apple Support