This approach attempts to ensure that the log for each connection is
complete before the next sequence of states begins.

Updates #32329

Change-Id: I25150d3ceab6568af56a40d2b14b5f544dc87f61
Reviewed-on: https://go-review.googlesource.com/c/go/+/210717
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>