Validate that one of streams choosen in logs on api side

Fixes #6506

There is the bug, that very hard to fix: When we return job.Errorf in
"logs" job it writes to job.Stderr, to which connected ResponseWriter and on
this write w.WriteHeader(http.StatusOK) is called. So, we get 200 on error
from "logs" job.
Why isn't this returning an error?