[bug] Navigating back loses 'working on it' — the run is still going and the API already reports it #252

The symptom

Start work, navigate away, come back — "working on it" is gone. The agent may still be working; the
console simply stops claiming so. There is no way to tell a finished run from a running one.

It is entirely client-side, and the data already exists

The thinking indicator is local React state. pages/InstanceDetail.tsx:

:80    const [thinking, setThinking] = useState(false);
:327   setThinking(true);      // on send
:352   setThinking(false);     // when the reply lands

Never seeded from the server. Unmount discards it; remount starts at false.

The loop watcher only knows about loops this tab started. pollLoop opens with:

if (!id || !loopRunIdRef.current) return;

loopRunIdRef is set when you press Loop in that tab. After a remount it is null, so the
watcher returns immediately every tick — even with a run active.

But the server can answer this already:

Nothing needs building on the backend. The Assistant tab just never asks on mount.

And the one UI that does show runs is in the wrong place

LoopRunsSection — the component that lists loop runs — is rendered only in
SettingsTab.tsx:1145. So the answer to "is my agent working?" lives in Settings, several clicks
from the Assistant tab where the work was started and where the user is looking.

Proposal

• On mount, call GET /v1/instances/:id/loop; if a run is running, adopt its id into
  loopRunIdRef and resume the existing watcher. The polling machinery already works — it is only
  missing its starting value.
• Show a persistent indicator on the Assistant tab whenever a run is active, with the iteration
  count that pollLoop already reads.
• For a plain chat turn, seed the thinking state from the DO's own status rather than assuming
  idle. Note ensureStateDefaults (agent-do-prompt.ts:63) resets thinking/error → idle
  when the DO reloads, which is a sensible self-heal but means status is only trustworthy while
  the object is warm — so treat it as a hint, and let [bug] A chat turn is bound to the request — navigating away can lose the reply while its tool side effects persist #251 decide what "in flight" should durably
  mean for chat.
• Consider surfacing LoopRunsSection (or a compact form of it) where work happens, not only in
  Settings.

Verification

• Start a loop, navigate to another agent and back: the indicator and iteration count return
  without a page reload.
• Two tabs open on the same instance both show the run — neither "owns" it.
• A finished run clears on return rather than showing stale "working".