"Concise experienced advice" because you didn't back up? Don't blame it on the update. You're using an operating system well known for being very limited in its purpose, which is to ease people from MacOS or Windows into Linux. Not to use Brave Browser in it pretending to be something that it's not. In elementary OS you're largely supposed to stick to the "elementary applications". One of them is a web browser. (shrugs) If that is too limited, and the other programs in the suite, the user is supposed to choose another Linux OS such as Linux Mint.
Also the browsers you prefer to use are very complex things, and so is Chromium, Firefox, Opera and others. It's really difficult to keep things steady when there are also troublemakers wanting to make somebody sad such as computers unable to start into the desktop. Take it from me. I have Brave Browser on Manjaro MATE, it's the only thing I ever installed from the AUR. It is very slow, takes 1-1/2 minutes or longer only to start for the first time, trying to start any site at first in the session is very slow, and many other things it does such as ad-blocking are slow. It's because I'm trying to run it on an 11-year-old PC with a physical internal disk.
elementary OS comes with its own desktop environment called Pantheon which was based on GNOME. It's a giant mess, to say the least possible. I would like to read the advice of somebody who worked extensively with Brave Browser, say in Fedora or Ubuntu which comes with GNOME. Then it would be a good idea on how it would happen on Pantheon.
This is my last post on this topic. Because I cannot be more "concise" than that, and I don't want to tell you what is obvious (see the last words on the first paragraph).