### 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_MAIN_THREAD_GUARD;
	WARN_DEPRECATED_MSG(R"*(The "push_unhandled_input()" method is deprecated, use "push_input()" instead.)*");
	ERR_FAIL_COND(!is_inside_tree());
	ERR_FAIL_COND(p_event.is_null());
	local_input_handled = false;
	if (disable_input || !_can_consume_input_events()) {
		return;
	}
	if (Engine::get_singleton()->is_editor_hint() && get_tree()->get_edited_scene_root() && get_tree()->get_edited_scene_root()->is_ancestor_of(this)) {
		return;
	}
	Ref<InputEvent> ev;
	if (!p_local_coords) {
		ev = _make_input_local(p_event);
	} else {
		ev = p_event;
	}
	_push_unhandled_input_internal(ev);
}
#endif 
void Viewport::_push_unhandled_input_internal(const Ref<InputEvent> &p_event) {