If the online engine is unavailable
Even when you're online and signed in, your organisation's processing engine can itself be temporarily unreachable. When that happens the header shows a short notice — "Processing isn't set up yet" if it's never been configured for your organisation, or "Processing is temporarily unavailable" if it's down right now. Hovering the notice explains further: if part of the service is having trouble, "Some tools may not work right now"; if it can't be reached at all, "The processing service isn't responding. Your open work is safe; try again in a moment." Online-only tools behave the same as if you were offline until it recovers: they tell you they need a connection rather than failing partway through a job.
This notice only appears when there's actually a problem — a healthy connection to a healthy engine shows nothing at all in the header, so its absence is itself a good sign.