### Godot version

v4.1.dev.custom_build [18112ba36]

### System information

Linux Mint 21.1, NVIDIA GeForce GTX 1050 Ti,  Vulkan API 1.3.205

### Issue description

This is a regression from #64388. 

Textures seem to be used differently in 2D and 3D. They are rendered using the `RID` in 3D, and changing the `viewport_path` will cause the `RID` to change.

https://github.com/godotengine/godot/assets/30386067/ad393fe8-50c1-4a89-870d-58d4e224bcc6


### Steps to reproduce

1. Download and import MRP.
2. Open 1.tscn, and try to switch the `viewport_path` of the `MeshInstance3D:mesh:material:albedo_texture` in the MeshInstance3D node.
3. After switching, the MeshInstance3D is rendered as white in the editor;
4. Close and then reopen 1.tscn.

### Minimal reproduction project

[ViewportTexture-change-viewport_path.zip](https://github.com/godotengine/godot/files/11509010/ViewportTexture-change-viewport_path.zip)

return false;
}
Ref<Image> ViewportTexture::get_image() const {
	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(path);
	ERR_FAIL_COND_MSG(!vpn, "ViewportTexture: Path to node is invalid.");
	vp = Object::cast_to<Viewport>(vpn);
	ERR_FAIL_COND_MSG(!vp, "ViewportTexture: Path to node does not point to a viewport.");
	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);
	} else {
		ERR_FAIL_COND(proxy.is_valid()); 
		proxy = RS::get_singleton()->texture_proxy_create(vp->texture_rid);
	}
	vp_pending = false;
	emit_changed();
}
void ViewportTexture::_bind_methods() {