> If anything, async-await feels like an extremely non-functional thing to begin with

Futures/promises (they mean different things in different languages), like many other things, form monads. In fact async-await is a specialization of various monad syntactic sugars that try to eliminate long callback chains that commonly affect many different sorts of monads.

Hence things like Haskell's do-notation are direct precursors to async-await (some libraries such as Scala's monadless https://github.com/monadless/monadless make it even more explicit, there lift and unlift are exactly generalized versions of async and await).

To see how async-await might be generalized, one could turn to various other specializations of the same syntax, e.g. an async that denotes a random variable and an await that draws once from the random variable.

To see the correspondence with a flatMap method (which is the main component of a monad), it's enough to look at the equivalent callback-heavy code and see that it looks something like

  Future(5)
    .flatMap(x ->
      doSomethingFutureyWithX(x)
        .flatMap(lookItsAnotherCallback)
    )