agent web UI: keep the turn-state badge live instead of freezing until reload

The status badge's elapsed-time text ('thinking Xm Ys') was computed
from Date.now() inside the render function, so it only ever advanced
when the component actually re-rendered. Two gaps let it go stale:

- useAgentState's poll loop is a chained setTimeout, which browsers
  throttle (or suspend outright) once the tab is backgrounded, so
  polling could stall for a long time with no way back to a live
  reading short of a full page reload.
- even under healthy polling, the age text only advanced once every
  ~4s (the poll interval) instead of counting up smoothly.

Fix: resync immediately on visibilitychange (so returning to a
backgrounded tab doesn't leave a stale reading), and drive the age
text off its own 1s interval independent of the poll cadence.

frontend/packages/agent/src/Root.tsx

@@ -72,6 +72,17 @@ export function Root() {
   const [openPanel, setOpenPanel] = useState<OpenPanel>(null);
   const liveStreamRef = useRef<LiveStreamHandle>(null);
 
+  // Ticks the status badge's "thinking Xm Ys" age once a second,
+  // independent of the ~4s `/api/state` poll cadence — without its own
+  // clock the age text only advances when a poll happens to land, so it
+  // visibly stair-steps instead of counting up, and freezes outright for
+  // however long a poll is delayed (e.g. a backgrounded tab).
+  const [now, setNow] = useState(() => Date.now());
+  useEffect(() => {
+    const id = setInterval(() => setNow(Date.now()), 1000);
+    return () => clearInterval(id);
+  }, []);
+
   // Browser tab title — ports app.js's setHeader logic verbatim: prefer
   // the human display name + hive_name ("iris // pr1ma") so tabs read
   // naturally; fall back to the qualified domain label for multi-hive
@@ -175,7 +186,7 @@ export function Root() {
   // idle/thinking reading from before the harness went offline).
   const effectiveTurnState = state.status === 'online' ? state.turn_state : 'offline';
   const turnDef = STATE_LABELS[effectiveTurnState] ?? { glyph: '○', text: 'offline', tone: 'negative' as BadgeTone };
-  const stateAge = fmtAge(Date.now() - state.turn_state_since * 1000);
+  const stateAge = fmtAge(now - state.turn_state_since * 1000);
   // Consolidated status badge (mara: "why do we have separate alive
   // badge? ... one badge that shows thinking / idle / paused").
   // Not online → the alive-table's own reading (rate-limited/needs-login/