### Godot version

4.0.beta12

### System information

Windows 11, RTX 3080

### Issue description

When a Window Node is created with it's Transparent flag set to true and Project Settings --> Display --> Window --> Subwindows --> Embed Subwindows is false, the Window has a black background. By cycling the transparent flag from false and back to true again, during runtime, the window's background then becomes transparent. 

### Steps to reproduce

Attempt to create a Non-embedded Subwindow with a transparent background using the appropriate flags. 

### Minimal reproduction project

Note: this project is from Reddit user [gongpha](https://www.reddit.com/user/gongpha/) and his Reddit post [Learning a Godot 4.0 Window node](https://www.reddit.com/r/godot/comments/xr8yxn/learning_a_godot_40_window_node/)

https://github.com/gongpha/godot4-window-test
return "Windows";
}
void DisplayServerWindows::_set_mouse_mode_impl(MouseMode p_mode) {
	if (windows.has(MAIN_WINDOW_ID) && (p_mode == MOUSE_MODE_CAPTURED || p_mode == MOUSE_MODE_CONFINED || p_mode == MOUSE_MODE_CONFINED_HIDDEN)) {
		
		WindowID window_id = _get_focused_window_or_popup();
		if (!windows.has(window_id)) {
			window_id = MAIN_WINDOW_ID;
		}
		WindowData &wd = windows[window_id];
		RECT clipRect;
		GetClientRect(wd.hWnd, &clipRect);
		ClientToScreen(wd.hWnd, (POINT *)&clipRect.left);
		ClientToScreen(wd.hWnd, (POINT *)&clipRect.right);
		ClipCursor(&clipRect);
		if (p_mode == MOUSE_MODE_CAPTURED) {
			center = window_get_size() / 2;
			POINT pos = { (int)center.x, (int)center.y };
			ClientToScreen(wd.hWnd, &pos);