Tell Sentry about all raised Responses

And tag sentry entries with a response code (1xx, 2xx, ... 5xx, n/a).
We're using barely any of our sentry quota, so we may as well start
logging more stuff there (assuming it doesn't affect performance, but
I can't imagine that sentry is our bottleneck).

This came up because we were trying to debug a 403 that @zwn is seeing
with trying to update his take. We're not sure where it's coming from
and right now we're not even sending that to stdout. With this change we
should at least an exception reference ID on stdout and the full info in
Sentry.