Funny enough, I had all those issues withe the native version. Installing via Flatpak solved all the glitches, and I just update via Discover.
Problem now is hardware video decoding stubbornly refuses to work at all.
You have to be clearer, you should give us more details, what is the distribution, the window manager you are using, its version, if you have an old computer it could depend on Wayland, if you don’t use Xorg as a window system, I know there are problems with the new versions of gnome on old computers, which uses Wayland as as default, in the latest version of gnome, but I think it can be solved by going back to Xorg, but you have to inform yourself well. Then you have to tell us if you uses the stable version of Brave, because the beta version has problems displaying some sites and I had to uninstall it. Usually the native installation does not give problems, if the problem is not of the display manager itself or the linux version. I don’t understand what you mean by “I just update via Discover”, flatpack is updated via the terminal, with the “flatpak update” command, or via the gnome “Software” package manager. The native package depends of the distribution you use, in Debian or ubuntu you also use apt or apt-get etc. from the terminal.