### 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.
ClassDB::bind_method(D_METHOD("set_viewport_path_in_scene", "path"), &ViewportTexture::set_viewport_path_in_scene);
	ClassDB::bind_method(D_METHOD("get_viewport_path_in_scene"), &ViewportTexture::get_viewport_path_in_scene);
	ADD_PROPERTY(PropertyInfo(Variant::NODE_PATH, "viewport_path", PROPERTY_HINT_NODE_PATH_VALID_TYPES, "Viewport", PROPERTY_USAGE_DEFAULT | PROPERTY_USAGE_NODE_PATH_FROM_SCENE_ROOT), "set_viewport_path_in_scene", "get_viewport_path_in_scene");
}
ViewportTexture::ViewportTexture() {
	set_local_to_scene(true);
}
ViewportTexture::~ViewportTexture() {
	if (vp) {
		vp->viewport_textures.erase(this);
	}
	ERR_FAIL_NULL(RenderingServer::get_singleton());
	if (proxy_ph.is_valid()) {
		RS::get_singleton()->free(proxy_ph);
	}
	if (proxy.is_valid()) {
		RS::get_singleton()->free(proxy);
	}
}
void Viewport::_process_dirty_canvas_parent_orders() {