Wow. I do not think I have had to install keys in my PureOS environment except for the one foreign repository I use for a sailing application and my VPN. I am not sure how to help with Byzantium keys. Are they listed in /etc/apt/trusted.gpg.d (*.gpg)? You won’t be able to see the contents, but are they there?
I think you should be seeing something in that Software and Updates graphical interface. I tried the same apt-key list command you did, even though it is deprecated. (It is still in Debian 11 and in Byzantium.) I see the same keys as listed in Software and Updates.
I looked at your output from above. I just do not see any of these apt-key errors that you are getting from Byzantium when updating, so something fundamental is wrong.
I also noticed Brave does not have a key. You may want to start here. Although that link is pretty old, it might point you in the right direction for that one. (I do not use Brave. You might want to check these fora for more information on it and how to install it.)
I see a VPN for you too. Mine had a package that set everything up, and it seems to have bypassed the authentication I mentioned before. Maybe that is a hint. It did add a key to the gpg ring. (gpg --list-public-keys; don’t post the output.)
Fortunately, a lot more knowlegable people than I look at these topics. I was kind of hoping it would be just a foreign repository problem.
PS. Are these packages installed?
debian-archive-keyring/byzantium,byzantium,now 2021.1.1
debian-keyring/byzantium,byzantium,now 2021.07.26
pureos-archive-keyring/byzantium,byzantium,now 2021.11.0