It looks like Chromium (the browser that Brave is based on) stopped supporting Windows 8.1 earlier this year, with the last supported version being Chromium 109.
Although it seems that Chromium will keep giving security updates until October, I’m not sure if Brave is also incorporating those updates into their browser, or if they are no longer maintaining a version based on Chromium 109.
If you are getting a notification telling you that there are no updates available, it is likely that the latter is true.
No support, like it was a big deal for the developers, but all what matters are Microsoft Profits for forcing users to migrate to the newest OS. Bye then