On Fedora 40, if you have darkmode set to the default in GNOME, GNU Emacs does not follow the darkmode styling directive for the menu bar. I spent forever trying to make this work in darkmode. If the app is launched using $ GTK_THEME=Adwaita:dark emacs it will start with the menu bar set to dark mode.

However there is a script that actually launches Emacs in /user/bin/emacs-desktop. If you open that file and modify it by adding export GTK_THEME=Adwaita:dark emacs just before the last line, it will launch with darkmode enabled. This is the entire contents of that file:

#!/usr/bin/sh

# The pure GTK build of emacs is not supported on X11, so try to avoid
# using if there is an alternative.

if [ "$XDG_SESSION_TYPE" = 'x11' ]; then
    case "$(readlink -f /usr/bin/emacs)" in
    */emacs-*.*-pgtk)
        if type emacs-gtk+x11 >/dev/null; then
            exec emacs-gtk+x11 "$@"
        elif type emacs-lucid >/dev/null; then
            exec emacs-lucid "$@"
        fi
        ;;
    esac
fi

export GTK_THEME=Adwaita:dark emacs
exec emacs "$@"

I’m not claiming it is the right way. It just worked when I tried it.