I also have version 1.77.100 and get the same browser not supported error. Tried clearing all browser data, log in private window without any extension enabled, restarting PC, using a VPN and turning it off again etc. None of that worked. But what worked for me was creating an entirely new profile. This suggests some profile data is corrupted or setting is misbehaving due to an update of the browser or the OS.
After many testing and trials, I have narrowed it down to simply Twitch misbehaving with Brave’s graphics/hardware acceleration setting in the browser. I have to keep this setting enabled to log in to Twitch. Note that I also had to clear browser cache/cookies after toggling it on and restarting the browser (fully closing and opening again, not relaunch) in order to be able to log in (was able to replicate this much easier using private window).