I had the same issue, my computer settings gave permission and could not find a single issue yet I did not have permission on Discord in Opera while I did on discord computer app. If you go into the discord app in opera - settings - voice and video - you will be here. Then click on the tiny translucent mic up the very top and a little menu will pop down. Here you can give permission.

The other option is to open discord website in the opera browser, log in while using the browser (not opening app), and then a pop up will appear to ask permission. Say yes and this will also fix the issue