NOTICE: This extension no longer exists, making this answer outdated. The answer however has been left intact as-is for historical reasons. It is suggested that you attempt to use other mechanisms to achieve this goal, rather than this plugin.
If this fact matter, I'm the author of the extension:
I can not speak for ubuntu or gnome developers, but as you already note there are not any official implementation available for gnome-shell or the ubuntu-session.
The Gnome-Global-AppMenu extension is supported in Ubuntu 18.04 (X11 session) better than ever.
My desition to discontinued Gnome-Global-AppMenu was base on severals facts that are not really valid rigth now, for that reason the Gnome-Global-AppMenu is not discontinued rigth now, besides that, it have improvements.
The Gnome-Global-AppMenu is now using (as a user decision) the fork of unity-gtk-module called appmenu-gtk-module. This is the same fork that is used in Mate and XFCE. Also the jayanta support was improved to really work and more things was added.
After a lot of time inverted to underestand how Gtk, Gnome shell and also unity-gtk-module works around the global menu, with the developer of this fork called appmenu-gtk-module, we were able to create some funtional code for handled the Gtk Wayland windows. Here is the original code that you can install and test from the source:
Personally, I'm also want to contribute to enhance more the Wayland support for the Gtk applications inside the appmenu-gtk-module, because the appmenu-gtk-module have just an initial support for the Gtk-Wayland.
Develop something is for me a pleasure and will not be ever an obligation. So, nothing of that means that i will promise not discontinued the develop of this extension or something like that. But also if that happens, the code is and will be aviable for the developers that want to continue with it.
You can check for yourself all that things if you install the extension from his official site in gitlab. Issues can be reported also there.