### 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)

Vector2 subwindow_drag_pos;
		Rect2i subwindow_drag_close_rect;
		bool subwindow_drag_close_inside = false;
		SubWindowResize subwindow_resize_mode;
		Rect2i subwindow_resize_from_rect;
		Vector<SubWindow> sub_windows; 
	} gui;
	DefaultCanvasItemTextureFilter default_canvas_item_texture_filter = DEFAULT_CANVAS_ITEM_TEXTURE_FILTER_LINEAR;
	DefaultCanvasItemTextureRepeat default_canvas_item_texture_repeat = DEFAULT_CANVAS_ITEM_TEXTURE_REPEAT_DISABLED;
	bool disable_input = false;
	bool _gui_call_input(Control *p_control, const Ref<InputEvent> &p_input);
	void _gui_call_notification(Control *p_control, int p_what);
	void _gui_sort_roots();
	Control *_gui_find_control_at_pos(CanvasItem *p_node, const Point2 &p_global, const Transform2D &p_xform);
	void _gui_input_event(Ref<InputEvent> p_event);
	void _perform_drop(Control *p_control = nullptr, Point2 p_pos = Point2());
	void _gui_cleanup_internal_state(Ref<InputEvent> p_event);
	void _push_unhandled_input_internal(const Ref<InputEvent> &p_event);
	Ref<InputEvent> _make_input_local(const Ref<InputEvent> &ev);
	friend class Control;
	List<Control *>::Element *_gui_add_root_control(Control *p_control);
	void _gui_remove_root_control(List<Control *>::Element *RI);
	String _gui_get_tooltip(Control *p_control, const Vector2 &p_pos, Control **r_tooltip_owner = nullptr);
	void _gui_cancel_tooltip();
	void _gui_show_tooltip();
	void _gui_remove_control(Control *p_control);
	void _gui_hide_control(Control *p_control);
	void _gui_force_drag(Control *p_base, const Variant &p_data, Control *p_control);
	void _gui_set_drag_preview(Control *p_base, Control *p_control);
	Control *_gui_get_drag_preview();