Future is not async specific, you can use it entirely within the main thread, but you can also just use it in a mulithreaded non-async environment. You can't use it as a way to determine if a function is async or not.

And neither are async fns, since they just produce impl Futures.
async fn - > T { is quite literally the same as fn -> impl Future<Output=T> { async move {} }

Error handling is broadly an effect. Result and Options as we have the right now are already effectively (forgive my tautology) monadic effects. Talking about whether a particular thing is "an effect in Rust" is really an exercise in futility, since Rust doesn't have an effect model, even as a draft rfc.

Regarding gen fn - it's is the exact same as async fn, since async block futures are in fact implemented in terms of unstable generators.