a paused job shows a pause icon, not a spinner

The details panel kept spinning after Pause, so a frozen dev server looked like a
working one. The spinner is the whole claim being made, and it was false — the
state most likely to be watched, since the panel is where you sit while a `bun dev`
runs.

Amber either way: it is still a live job holding its port and its memory, which is
what separates paused from stopped. What changes is the motion, and the line beside
it now reads `paused` rather than `running…`.

── And the state moved up a level ──

`paused` lived in the panel, which unmounts when you close it. Closing and
reopening would have put a spinning icon back over a stopped process — the exact
failure this commit is fixing, arriving by a different route. It is the tray's now,
so it survives the panel being closed.

Still per-session: a reload forgets, and the button then offers Pause on a job that
is already frozen. SIGSTOP makes that harmless, and the honest fix is asking the
process rather than remembering — `ps -o state=` on the pids holding the output
file would make it survive anything, at the cost of a spawn per poll. Worth doing
if this ever misleads.

The chip is unchanged: a paused job still shows the running dot there, because live
is what that dot means and the distinction belongs where the controls are.

tsgo clean, frontend builds, 914 pass / 7 fail unchanged.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/workspaces/officerdev/src/apps/Chat/components/BackgroundTaskTray.tsx

@@ -37,6 +37,15 @@ export const BackgroundTaskTray = ({ messages, sessionId }: BackgroundTaskTrayPr
   const { tasks, pinned, unpinned, running, clearable, togglePin, dismiss, dismissFinished } =
     useBackgroundTasks(messages);
   const [openId, setOpenId] = useState<string | null>(null);
+  /**
+   * Which jobs are frozen.
+   *
+   * Held here rather than in the panel because the panel unmounts when you close it, and a `paused` that
+   * resets would put a spinning icon over a stopped process — the exact thing this display is for. Still
+   * per-session: a reload forgets, and the button then says Pause over an already-frozen job, which
+   * SIGSTOP makes harmless.
+   */
+  const [pausedIds, setPausedIds] = useState<string[]>([]);
   const client = useClient();
 
   /**
@@ -91,6 +100,7 @@ export const BackgroundTaskTray = ({ messages, sessionId }: BackgroundTaskTrayPr
     try {
       const result = await client.post<{ ok: boolean; reason?: string }>(`/chat/tasks/${taskId}/pause`, { paused });
       if (!result.ok) toast.error(result.reason ?? 'Could not pause that job');
+      else setPausedIds((prev) => (paused ? [...new Set([...prev, taskId])] : prev.filter((id) => id !== taskId)));
       return result.ok;
     } catch (err) {
       toast.error(err instanceof Error ? err.message : 'Could not pause that job');
@@ -123,6 +133,7 @@ export const BackgroundTaskTray = ({ messages, sessionId }: BackgroundTaskTrayPr
           onClose={() => setOpenId(null)}
           onStop={open.status ? undefined : () => void stopTask(open.taskId)}
           onPause={(next) => pauseTask(open.taskId, next)}
+          paused={pausedIds.includes(open.taskId)}
           onRestart={() => void restartTask(open.taskId)}
         />
       )}
@@ -280,18 +291,16 @@ type TaskPanelProps = {
   onStop?: () => void;
   /** Freeze and thaw the process. Present while it is running; the label follows the state. */
   onPause?: (paused: boolean) => Promise<boolean>;
+  /** Frozen right now — owned by the tray, so closing this panel does not forget it. */
+  paused?: boolean;
   /** Run the command again, whether it is running or long finished. */
   onRestart?: () => void;
   task: BackgroundTask;
   onClose: () => void;
 };
 
-const TaskPanel = ({ task, onClose, onStop, onPause, onRestart }: TaskPanelProps) => {
+const TaskPanel = ({ task, onClose, onStop, onPause, onRestart, paused = false }: TaskPanelProps) => {
   const running = !task.status;
-  // Local, because a paused process is a short-lived state somebody is watching. It resets on reload,
-  // which is honest enough: SIGCONT is idempotent, and the button says what it will do rather than what
-  // it believes has happened.
-  const [paused, setPaused] = useState(false);
   const { data, isLoading } = useTaskDetail(task.taskId, running);
   const bodyRef = useRef<HTMLDivElement | null>(null);
   const pinnedRef = useRef(true);
@@ -309,10 +318,18 @@ const TaskPanel = ({ task, onClose, onStop, onPause, onRestart }: TaskPanelProps
         <div className="min-w-0 flex-1">
           <div className="truncate text-xs text-foreground/80">{task.description || 'Background task'}</div>
           <div className="truncate text-xs text-muted-foreground">
-            {task.taskType ?? 'task'} · {task.status ? (task.summary ?? task.status) : 'running…'}
+            {task.taskType ?? 'task'} · {task.status ? (task.summary ?? task.status) : paused ? 'paused' : 'running…'}
           </div>
         </div>
-        {running && <Loader2 className="h-3.5 w-3.5 shrink-0 animate-spin text-warning" />}
+        {/* A frozen process is not a working one, and a spinner says it is. Same amber either way — it is
+            still a live job holding its port and its memory — but STILL, because the animation is the
+            whole claim being made. */}
+        {running &&
+          (paused ? (
+            <Pause className="h-3.5 w-3.5 shrink-0 text-warning" />
+          ) : (
+            <Loader2 className="h-3.5 w-3.5 shrink-0 animate-spin text-warning" />
+          ))}
         {/* Labelled here, unlike the chip's icon-only version. The panel is where you come to decide
             whether to keep something running, so the control that ends it should not be a glyph you
             have to hover to identify. */}
@@ -321,10 +338,7 @@ const TaskPanel = ({ task, onClose, onStop, onPause, onRestart }: TaskPanelProps
         {running && onPause && (
           <button
             type="button"
-            onClick={async () => {
+            onClick={() => void onPause(!paused)}
-              const next = !paused;
-              if (await onPause(next)) setPaused(next);
-            }}
             title={paused ? 'Let it continue where it left off' : 'Freeze the process, keeping its state'}
             className="flex shrink-0 cursor-pointer items-center gap-1 rounded border border-border px-2 py-1 text-xs text-muted-foreground transition-colors hover:border-warning/40 hover:text-warning"
           >