Functional languages are perfectly capable languages so you can typically use them for anything you'd use any other language for. But if you want a project that specifically showcases functional programming, writing a parser using parser combinators can be fun and instructive.

I don't like to think of a lot of these languages in terms of "functional". Haskell specifically does follow a functional paradigm, but Erlang/Elixir is more about the actor model and the functional aspects support that.