Currently a write error will cause future reads to return that same error.
However, there may have been extra information from a peer pending on
the read direction that is now unavailable.

This change splits the single connErr into errors for the read, write and
handshake. (Splitting off the handshake error is needed because both read
and write paths check the handshake error.)

Fixes #7414.

LGTM=bradfitz, r
R=golang-codereviews, r, bradfitz
CC=golang-codereviews
https://golang.org/cl/69090044