### 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)

class Label;
class SceneTreeTimer;
class Viewport;
class Window;
class World2D;
class ViewportTexture : public Texture2D {
	GDCLASS(ViewportTexture, Texture2D);
	NodePath path;
	friend class Viewport;
	Viewport *vp = nullptr;
	bool vp_pending = false;
	void _setup_local_to_scene(const Node *p_loc_scene);
	mutable RID proxy_ph;
	mutable RID proxy;
protected:
	static void _bind_methods();
public:
	void set_viewport_path_in_scene(const NodePath &p_path);
	NodePath get_viewport_path_in_scene() const;
	virtual void setup_local_to_scene() override;
	virtual int get_width() const override;
	virtual int get_height() const override;
	virtual Size2 get_size() const override;
	virtual RID get_rid() const override;
	virtual bool has_alpha() const override;
	virtual Ref<Image> get_image() const override;
	ViewportTexture();
	~ViewportTexture();
};
class Viewport : public Node {