Maybe I am misunderstanding the question but it seems like there were/are various bots at work here, but in principle a "single" bot could do these things, and is certainly how they handled animation. But even a single bot could be running many times over, or be otherwise multi-threaded.

It does seem important that as far as the page was concerned you couldn't, say, check two boxes at the exact same time. So whatever work they did to coordinate the animations had to happen through tons of single requests.