If it’s any comfort to you, you can trust the maintainer of the AUR package, it is maintained by Rafael Fontenelle
who is one of the coordinators of the GNOME pt_BR translation team and is also the admin of the GNOME Brasil group on Telegram, we were talking about this today and he promptly updated the AUR packages for anyone interested, there is no confusion about the two packages, what you need to install on the system is gnome-browser-connector the browser extension is the one that is normally installed in the firefox or chrome browser store.
As for the problem with the extensions site, the problem was in the site’s infrastructure not being influenced by the chrome-gnome-shell connector.
