Better handle ResponseEmitter closure in `Emit`

We need to make it clear whether the emitter is simply closed (and the sender should go away) or something actually went wrong.

Really, we should probably just *log* what went wrong and return a boolean where `false` means "closed". Currently, we return an error but it's unclear how this error should be handled. Should the caller follow up with a `SetError` call? (the answer is no but the API is really unclear).

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Also, we need to make sure that all emitters handle context cancellation correctly.