When I use gtk_application_set_menubar() the menus appear in the MacOS menubar - as expected. However, on startup, they are not “active” - i.e. they do not respond to clicks by opening up the menu with menu items as I would expect (and as it does when I run the same program on my Ubuntu system). For me, gtk-demo-application also has an unresponsive menu in the menubar - and that seems to me not to be the intended behavior.
However, if I click off the application so that the Finder takes over the MacOS menubar, then click on the application again, so that it has focus, then the menu becomes active and I can open the menu items.
The installation of GTK4 that I am using on MacOS is provided by Homebrew.