### 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.
if (!vp) {
		if (!vp_pending) {
			ERR_PRINT("Viewport Texture must be set to use it.");
		}
		return Ref<Image>();
	}
	return RS::get_singleton()->texture_2d_get(vp->texture_rid);
}
void ViewportTexture::_setup_local_to_scene(const Node *p_loc_scene) {
	Node *vpn = p_loc_scene->get_node_or_null(path);
	ERR_FAIL_NULL_MSG(vpn, "Path to node is invalid: '" + path + "'.");
	vp = Object::cast_to<Viewport>(vpn);
	ERR_FAIL_NULL_MSG(vp, "Path to node does not point to a viewport: '" + path + "'.");
	vp->viewport_textures.insert(this);
	ERR_FAIL_NULL(RenderingServer::get_singleton());
	if (proxy_ph.is_valid()) {
		RS::get_singleton()->texture_proxy_update(proxy, vp->texture_rid);
		RS::get_singleton()->free(proxy_ph);
		proxy_ph = RID();
	} else {
		ERR_FAIL_COND(proxy.is_valid()); 
		proxy = RS::get_singleton()->texture_proxy_create(vp->texture_rid);
	}
	vp_pending = false;
	vp_changed = false;
	emit_changed();
}
void ViewportTexture::_bind_methods() {