### 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)

if (gui.mouse_over) {
		_gui_call_notification(gui.mouse_over, Control::NOTIFICATION_MOUSE_EXIT);
		gui.mouse_over = nullptr;
	}
}
void Viewport::_drop_mouse_focus() {
	Control *c = gui.mouse_focus;
	BitField<MouseButtonMask> mask = gui.mouse_focus_mask;
	gui.mouse_focus = nullptr;
	gui.forced_mouse_focus = false;
	gui.mouse_focus_mask.clear();
	for (int i = 0; i < 3; i++) {
		if ((int)mask & (1 << i)) {
			Ref<InputEventMouseButton> mb;
			mb.instantiate();
			mb->set_position(c->get_local_mouse_position());
			mb->set_global_position(c->get_local_mouse_position());
			mb->set_button_index(MouseButton(i + 1));
			mb->set_pressed(false);
			mb->set_device(InputEvent::DEVICE_ID_INTERNAL);
			c->_call_gui_input(mb);
		}
	}
}
void Viewport::_drop_physics_mouseover(bool p_paused_only) {