Also added a test to ensure that any interactions
between TimeoutHandler and Flusher result in the
correct status code and body, but also that we don't
get superfluous logs from stray writes as was seen
in the bug report.

Fixes #34439.

Change-Id: I4af62db256742326f9353f98a2fcb5f71d2a5fd9
Reviewed-on: https://go-review.googlesource.com/c/go/+/197659
Run-TryBot: Emmanuel Odeke <emm.odeke@gmail.com>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>