It does look like severe etching of the lacquer coat caused by bird poo.
I doubt that claying will improve it - claying will remove embedded contaminants, but if it’s the lacquered surface that’s etched, there’s nothing embedded to remove.
Machine polishing with an appropriate combination of pad and polish should remove it - that’s assuming you are dealing with etching. I’ve successfully corrected quite a large area of etching caused by a pigeon using my car for target practice on a very hot sunny day. The pigeon poo baked hard on the car (was only on the car for no more than a 1/2 hour), and after soaking it and carefully removing it, there was some serious etching. After 15-20 minutes with my DA polisher, all signs of etching were removed.