Almost all webhook tests use this helper, except a few
webhooks that write to private streams.
Being concise is important here, and the name
`self.send_and_test_stream_message` always confused
me, since it sounds you're sending a stream message,
and it leaves out the webhook piece.
We should consider renaming `send_and_test_private_message`
to something like `check_webhook_private`, but I couldn't
decide on a great name, and it's very rarely used. So
for now I just made sure the docstrings of the two
sibling functions reference each other.