### 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)

#include "viewport.h"
#include "core/config/project_settings.h"
#include "core/core_string_names.h"
#include "core/debugger/engine_debugger.h"
#include "core/object/message_queue.h"
#include "core/string/translation.h"
#include "core/templates/pair.h"
#include "core/templates/sort_array.h"
#include "scene/2d/audio_listener_2d.h"
#include "scene/2d/camera_2d.h"
#include "scene/2d/collision_object_2d.h"
#ifndef _3D_DISABLED
#include "scene/3d/audio_listener_3d.h"
#include "scene/3d/camera_3d.h"
#include "scene/3d/collision_object_3d.h"
#include "scene/3d/world_environment.h"
#endif 
#include "scene/gui/control.h"
#include "scene/gui/label.h"
#include "scene/gui/popup.h"