Yes and no. On Wayland an app has no access to its context. I.e. location on the screen, or ability to move itself. So dragging by the title bar is the composit

Yes and no. On Wayland an app has no access to its context. I.e. location on the screen, or ability to move itself. So dragging by the title bar is the compositor/WMs job. That means the WM has to know where those higher level controls are. It's also not really an applications job to manage its look as in themes. Is it the toolkits job or the compositor/wm?