### 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)

} break;
		case NOTIFICATION_VP_MOUSE_EXIT: {
			gui.mouse_in_viewport = false;
			_drop_physics_mouseover();
			_drop_mouse_over();
			_gui_cancel_tooltip();
			
			
			
		} break;
		case NOTIFICATION_WM_WINDOW_FOCUS_OUT: {
			_gui_cancel_tooltip();
			_drop_physics_mouseover();
			if (gui.mouse_focus && !gui.forced_mouse_focus) {
				_drop_mouse_focus();
			}
			
			
			
			
		} break;
		case NOTIFICATION_PREDELETE: {
			if (gui_parent) {
				gui_parent->gui.tooltip_popup = nullptr;
				gui_parent->gui.tooltip_label = nullptr;
			}
		} break;
	}
}
void Viewport::_process_picking() {