### 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)

void push_text_input(const String &p_text);
	void push_input(const Ref<InputEvent> &p_event, bool p_local_coords = false);
#ifndef DISABLE_DEPRECATED
	void push_unhandled_input(const Ref<InputEvent> &p_event, bool p_local_coords = false);
#endif 
	void set_disable_input(bool p_disable);
	bool is_input_disabled() const;
	Vector2 get_mouse_position() const;
	void warp_mouse(const Vector2 &p_position);
	virtual void update_mouse_cursor_state();
	void set_physics_object_picking(bool p_enable);
	bool get_physics_object_picking();
	void set_physics_object_picking_sort(bool p_enable);
	bool get_physics_object_picking_sort();
	Variant gui_get_drag_data() const;
	void gui_reset_canvas_sort_index();
	int gui_get_canvas_sort_index();
	void gui_release_focus();
	Control *gui_get_focus_owner() const;
	PackedStringArray get_configuration_warnings() const override;
	void set_debug_draw(DebugDraw p_debug_draw);
	DebugDraw get_debug_draw() const;
	int get_render_info(RenderInfoType p_type, RenderInfo p_info);
	void set_snap_controls_to_pixels(bool p_enable);
	bool is_snap_controls_to_pixels_enabled() const;
	void set_snap_2d_transforms_to_pixel(bool p_enable);
	bool is_snap_2d_transforms_to_pixel_enabled() const;
	void set_snap_2d_vertices_to_pixel(bool p_enable);
	bool is_snap_2d_vertices_to_pixel_enabled() const;
	void set_input_as_handled();