I use gamescope on a separate TTY that directly launches either steam or heroic launcher. I find this works exceptionally well. No window manager needed as you are playing a game full screen anyway. It fixed some other things like HDR too but at a loss of the volume and brightness keys no longer working.
Don't know about gamescope, but the core of my own wine launch script is basically this:
if [ -z "$DISPLAY" ]; then
/usr/bin/startx /usr/bin/dbus-launch "$(readlink -f $0)" "$1" -- -layout singleLayout
fi
pw-cli i || (pipewire & sleep .5 ;\
pipewire-media-session &\
pipewire-pulse &)
cd "$DIR"
exec unshare -rcn $ENGINE "$IMAGE" $ARGS
and the rest of the script is about setting up the environment for the game: setting all the parameters used above, exporting the correct WINEPREFIX, mounting .iso's if required, etc.