I just went down a bit of a rabbit hole on YouTube but I can confirm there are other songs that people play on bagpipes! 😆
Apparently it's a bit hard as there aren't that many notes and the nature of them means you have to play notes constantly so you can't use pauses, but there's still a lot they can do.
There's Amazing Grace that you hear occasionally, but also stuff like:
https://youtube.com/watch?v=hDw9IHmgN4s