### 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 "scene/gui/popup_menu.h"
#include "scene/gui/subviewport_container.h"
#include "scene/main/canvas_layer.h"
#include "scene/main/window.h"
#include "scene/resources/mesh.h"
#include "scene/resources/text_line.h"
#include "scene/resources/world_2d.h"
#include "scene/scene_string_names.h"
#include "servers/audio_server.h"
#include "servers/rendering/rendering_server_globals.h"
void ViewportTexture::setup_local_to_scene() {
	if (vp_pending) {
		return;
	}
	Node *loc_scene = get_local_scene();
	if (!loc_scene) {
		return;
	}
	if (vp) {
		vp->viewport_textures.erase(this);
		vp = nullptr;
	}
	if (loc_scene->is_ready()) {
		_setup_local_to_scene(loc_scene);
	} else {
		loc_scene->connect(SNAME("ready"), callable_mp(this, &ViewportTexture::_setup_local_to_scene).bind(loc_scene), CONNECT_ONE_SHOT);
		vp_pending = true;
	}
}
void ViewportTexture::set_viewport_path_in_scene(const NodePath &p_path) {