### Godot version

4.0.3-stable

### System information

Windows 10

### Issue description

In some projects ViewportTexture remains pink and doesn't render viewport content after upgrading from 4.0.2-stable to 4.0.3-stable. If a pair of files viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable, problem goes away.

This is how it looks in 4.0.3-stable:
![4 0 3_stable_viewport_4 0 3](https://github.com/godotengine/godot/assets/1449921/44c191a9-4b67-4b02-90b6-4ab615f62a73)

And this is how it looks if viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable.
![4 0 3_stable_viewport_4 0 2](https://github.com/godotengine/godot/assets/1449921/f5abc605-f129-4222-9c0e-e9a07621dd9d)



### Steps to reproduce

Unfortunately, I cannot come up wit a simple demo project reproducing the problem. It exists in some projects and doesn't exist in others.


### Minimal reproduction project

Cannot produce a simple project reproducing the problem. In simple projects it works fine.
} break;
		case NOTIFICATION_VP_MOUSE_EXIT: {
			gui.mouse_in_viewport = false;
			_drop_physics_mouseover();
			_drop_mouse_over();
			_gui_cancel_tooltip();
			
			
			
		} break;
		case NOTIFICATION_WM_WINDOW_FOCUS_OUT: {
			_gui_cancel_tooltip();
			_drop_physics_mouseover();
			if (gui.mouse_focus && !gui.forced_mouse_focus) {
				_drop_mouse_focus();
			}
			
			
			
			
		} break;
		case NOTIFICATION_PREDELETE: {
			if (gui_parent) {
				gui_parent->gui.tooltip_popup = nullptr;
				gui_parent->gui.tooltip_label = nullptr;
			}
		} break;
	}
}
void Viewport::_process_picking() {