### 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)

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() {