### 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.
// SubViewports, that are used as Textures are not considered to be directly attached to screen.
	return Object::cast_to<SubViewportContainer>(get_parent()) && get_parent()->get_viewport() && get_parent()->get_viewport()->is_directly_attached_to_screen();
}
void SubViewport::_notification(int p_what) {
	ERR_MAIN_THREAD_GUARD;
	switch (p_what) {
		case NOTIFICATION_ENTER_TREE: {
			RS::get_singleton()->viewport_set_active(get_viewport_rid(), true);
			SubViewportContainer *parent_svc = Object::cast_to<SubViewportContainer>(get_parent());
			if (parent_svc) {
				parent_svc->recalc_force_viewport_sizes();
			}
		} break;
		case NOTIFICATION_EXIT_TREE: {
			RS::get_singleton()->viewport_set_active(get_viewport_rid(), false);
		} break;
	}
}
void SubViewport::_bind_methods() {