[AsyncStreaming] Explore using a `[Write/Read]Result` instead of an `EitherError`

Currently, the various read and write methods are using the `EitherError` type since we need to use typed throws but also account for different errors from the underlying writer and the closure that gets the spans. This isn't very ergonomic and it might be better to stop using throws all-together and instead explore introducing a new result-like type similar to the below:

```swift
enum WriteResult {
case success(Success)
case writeFailed(WriteFailure)
case producerFailed(Failure)
}
````