Update: I removed from Brave all extensions related to Google (Keep, Translate, save to Drive, etc.). This seems to have solved the problem.
I believe the source of the problem is related to Google login to extensions. I haven’t tested these extensions individually to see if they all cause the problem or if it’s just one or a few of them, but I’d assume it’s ever extension that requires a Google Account.
This is corroborated by the fact that creating a new Brave profile or reinstalling the browser does not solve the problem if the extensions are installed, but as soon as they are removed the problem stops.
For now, not having Brave opening a Google sign in page is reason enough for me to remove these extensions and use their respective webpages, but I doubt most people would feel the same way.