### 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)

AudioListener2D *get_audio_listener_2d() const;
	Camera2D *get_camera_2d() const;
	void set_as_audio_listener_2d(bool p_enable);
	bool is_audio_listener_2d() const;
	void update_canvas_items();
	Rect2 get_visible_rect() const;
	RID get_viewport_rid() const;
	void set_world_2d(const Ref<World2D> &p_world_2d);
	Ref<World2D> get_world_2d() const;
	Ref<World2D> find_world_2d() const;
	void enable_canvas_transform_override(bool p_enable);
	bool is_canvas_transform_override_enbled() const;
	void set_canvas_transform_override(const Transform2D &p_transform);
	Transform2D get_canvas_transform_override() const;
	void set_canvas_transform(const Transform2D &p_transform);
	Transform2D get_canvas_transform() const;
	void set_global_canvas_transform(const Transform2D &p_transform);
	Transform2D get_global_canvas_transform() const;
	virtual Transform2D get_final_transform() const;
	void assign_next_enabled_camera_2d(const StringName &p_camera_group);
	void gui_set_root_order_dirty();
	void set_transparent_background(bool p_enable);
	bool has_transparent_background() const;
	Ref<ViewportTexture> get_texture() const;