refactor: improve error storage for closed connections

[dignifiedquire]

No description provided.

[matheus23]

I don't super like that the tests change... But the way they change still kind of make sense, so maybe it's fine?

Is the difference between actual ConnectionErrors vs. TransportError and LocallyClosed maybe that anytime you get a ConnectionError it's the "negotiated" error between you and the other side? Whereas you can return LocallyClosed immediately when you call Connection::close() from somewhere else, and similarly you can return TransportError immediately once you realize the certificate doesn't match.
But it doesn't necessarily mean that the connection error is the one you "negotiated" with the other side if that makes sense. (Where "negotiated" means it's the final error of the connection after you've drained it to make sure the other side hasn't reported a possibly different error?)

[matheus23]

I really like this! We should squash-merge this IMO. (I have the minor nit above, but that's easy enough to fix)