Before this commit the connector waited for a completed response (via
ServerHttpResponse#setComplete or ServerHttpResponse#writeWith) or an
error signal in handling, but it didn't deal explicitly with the case
where both can occur.

This commit explicitly waits for the completion of handling (success
or error) before passing the response downstream. If an error occurs
after response completion, it is wrapped in a dedicated exception that
also provides access to the completed response.

Close gh-24051