I have had this problem as well. I restarted my Mac, rebooted Opera and went to a Meet.Google.com page. This time when the camera started I was given the MacOS alert boxes asking me to give permission to Opera. Once I did that, the browser appeared in my Security & Privacy panel. I feel like the apps don't appear in Security before you get the OS alert box. I'm also wondering if Opera asking me to give permission to the site interfered with the OS box.
So, a reboot helped.