### 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)

ERR_FAIL_COND(p_event.is_null());
	Ref<InputEventMouseButton> mb = p_event;
	if (mb.is_valid()) {
		if (!mb->is_pressed()) {
			gui.mouse_focus_mask.clear_flag(mouse_button_to_mask(mb->get_button_index())); 
		}
	}
}
List<Control *>::Element *Viewport::_gui_add_root_control(Control *p_control) {
	gui.roots_order_dirty = true;
	return gui.roots.push_back(p_control);
}
void Viewport::gui_set_root_order_dirty() {
	ERR_MAIN_THREAD_GUARD;
	gui.roots_order_dirty = true;
}
void Viewport::_gui_force_drag(Control *p_base, const Variant &p_data, Control *p_control) {
	ERR_FAIL_COND_MSG(p_data.get_type() == Variant::NIL, "Drag data must be a value.");
	gui.dragging = true;
	gui.drag_data = p_data;
	gui.mouse_focus = nullptr;
	if (p_control) {
		_gui_set_drag_preview(p_base, p_control);
	}
	_propagate_viewport_notification(this, NOTIFICATION_DRAG_BEGIN);
}
void Viewport::_gui_set_drag_preview(Control *p_base, Control *p_control) {