### 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_READ_THREAD_GUARD_V(SHADOW_ATLAS_QUADRANT_SUBDIV_DISABLED);
	ERR_FAIL_INDEX_V(p_quadrant, 4, SHADOW_ATLAS_QUADRANT_SUBDIV_DISABLED);
	return positional_shadow_atlas_quadrant_subdiv[p_quadrant];
}
Ref<InputEvent> Viewport::_make_input_local(const Ref<InputEvent> &ev) {
	if (ev.is_null()) {
		return ev; 
	}
	Transform2D ai = get_final_transform().affine_inverse();
	return ev->xformed_by(ai);
}
Vector2 Viewport::get_mouse_position() const {
	ERR_READ_THREAD_GUARD_V(Vector2());
	if (!is_directly_attached_to_screen()) {
		
		
		return gui.last_mouse_pos;
	} else if (DisplayServer::get_singleton()->has_feature(DisplayServer::FEATURE_MOUSE)) {
		return get_screen_transform_internal(true).affine_inverse().xform(DisplayServer::get_singleton()->mouse_get_position());
	} else {
		
		return get_screen_transform_internal().affine_inverse().xform(Input::get_singleton()->get_mouse_position());
	}
}
void Viewport::warp_mouse(const Vector2 &p_position) {