### 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 (!has_mouse_event) {
		
		
		
		Ref<InputEventMouseMotion> mm;
		mm.instantiate();
		mm->set_device(InputEvent::DEVICE_ID_INTERNAL);
		mm->set_position(get_mouse_position());
		mm->set_global_position(mm->get_position());
		mm->set_alt_pressed(Input::get_singleton()->is_key_pressed(Key::ALT));
		mm->set_shift_pressed(Input::get_singleton()->is_key_pressed(Key::SHIFT));
		mm->set_ctrl_pressed(Input::get_singleton()->is_key_pressed(Key::CTRL));
		mm->set_meta_pressed(Input::get_singleton()->is_key_pressed(Key::META));
		mm->set_button_mask(Input::get_singleton()->get_mouse_button_mask());
		physics_picking_events.push_back(mm);
	}
	while (physics_picking_events.size()) {
		Ref<InputEvent> ev = physics_picking_events.front()->get();
		physics_picking_events.pop_front();
		Vector2 pos;
		bool is_mouse = false;
		Ref<InputEventMouseMotion> mm = ev;
		if (mm.is_valid()) {
			pos = mm->get_position();
			is_mouse = true;
		}
		Ref<InputEventMouseButton> mb = ev;
		if (mb.is_valid()) {
			pos = mb->get_position();
			is_mouse = true;