### 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 (audio_listener_2d == p_listener) {
		return;
	} else if (audio_listener_2d) {
		audio_listener_2d->clear_current();
	}
	audio_listener_2d = p_listener;
}
void Viewport::_audio_listener_2d_remove(AudioListener2D *p_listener) {
	if (audio_listener_2d == p_listener) {
		audio_listener_2d = nullptr;
	}
}
void Viewport::_canvas_layer_add(CanvasLayer *p_canvas_layer) {
	canvas_layers.insert(p_canvas_layer);
}
void Viewport::_canvas_layer_remove(CanvasLayer *p_canvas_layer) {
	canvas_layers.erase(p_canvas_layer);
}
void Viewport::set_transparent_background(bool p_enable) {
	ERR_MAIN_THREAD_GUARD;
	transparent_bg = p_enable;
	RS::get_singleton()->viewport_set_transparent_background(viewport, p_enable);
}
bool Viewport::has_transparent_background() const {
	ERR_READ_THREAD_GUARD_V(false);
	return transparent_bg;
}
void Viewport::set_world_2d(const Ref<World2D> &p_world_2d) {