If your Mullvad Browser Flatpak is automatically logging you out as soon as you open it, here’s the fix.
sudo flatpak override --socket=wayland --env=MOZ_ENABLE_WAYLAND=1 net.mullvad.MullvadBrowser
This will force Mullvad Browser Flatpak to use Wayland and stop it from logging out automatically as by default it uses Xorg.
Cheers!