More specifically:

GetWindowForWidget() is the same for both aura and mus. So, said function should just removed and the calling sites can do what the functions is doing (it's a single line).

GetRootWindowControllerWithDisplayId() is different between the two implementations. I recommend moving this function onto Shell and having it delegate to WmShell. This way callers are calling the function directly on Shell.

More specifically for GetRootWindowControllerWithDisplayId() we should move this function to Shell. And change call sites to use Shell. Shell's implementation will call into WmShell::GetRootWindowForDisplayId(). e.g.

Shell::GetRootWindowControllerWithDisplayId(int64_t display_id) {
  WmWindow* root_window = wm_shell_->GetRootWindowControllerWithDisplayId(display_id);
  return root_window ? root_window->GetRootWindowController() : nullptr;
}

https://codereview.chromium.org/2726823003/