I see that you already ported your stuff to another browser, but it’s possible to downgrade Brave, probably in place, by downloading the .dmg of the last version that ran from the Releases site, dragging Brave to Applications, and launching. All of your stuff should still be there, unless you trashed the folder in your Library folder.
There’s still the matter of the autoupdates, though, and while there doesn’t seem to be a setting, you could try locking Brave in the Finder? That is, go to Applications, right-click or control-click Brave, and in the ensuing window, check the box next to Locked. In theory, that should prevent changes.
Also, it looks like the devs heard the users’ complaints, albeit too late for those using older OS. This is what I get in Nightly on Big Sur, now:
Also, you could try what I suggest in the rest of the post here:
Also, I know you’ve already ported, but one can successfully copy at least the Bookmarks file to other Chromium-based browsers. I’ve done it both ways successfully. In fact, I copied the bulk of my profile folder to Chromium and found most things to be okay, though I might have had to reinstall some extensions. The posts below might provide some help on where to find stuff.