fix(agent-status): let a stop's own inventory veto removal-driven done

Review finding round 5: after a restart the listener can miss a child's
start; another child's stop still lists it running in background_tasks.
A running non-teammate task or live shell/cron now vetoes the no-lead
removal->done into working. Veto only — folding the inventory at stop
time would reap a just-parked teammate row before its TeammateIdle
confirmation arrives.

src/shared/agent-hook-listener.test.ts

@@ -3177,6 +3177,40 @@ describe('shared agent-hook-listener', () => {
       expect(duplicatePark).toBeNull()
     })
 
+    it('keeps working when a no-lead stop carries an inventory with another live child', () => {
+      // Why: after a restart the listener can miss a2's start; a1's stop still
+      // lists a2 running in background_tasks — the removal must not retire it.
+      claudeEvent({
+        hook_event_name: 'SubagentStart',
+        agent_id: 'a1',
+        agent_type: 'general-purpose'
+      })
+      const stopped = claudeEvent({
+        hook_event_name: 'SubagentStop',
+        agent_id: 'a1',
+        background_tasks: [
+          { id: 'a2', type: 'subagent', status: 'running', agent_type: 'general-purpose' }
+        ]
+      })
+      // Why: veto only — a2's row materializes from its own events or the next
+      // lead Stop's fold; the stop must merely not retire the pane.
+      expect(stopped?.payload.state).toBe('working')
+    })
+
+    it('keeps working when a no-lead drain leaves a live shell in the inventory', () => {
+      claudeEvent({
+        hook_event_name: 'SubagentStart',
+        agent_id: 'a1',
+        agent_type: 'general-purpose'
+      })
+      const stopped = claudeEvent({
+        hook_event_name: 'SubagentStop',
+        agent_id: 'a1',
+        background_tasks: [{ id: 's1', type: 'shell', status: 'running' }]
+      })
+      expect(stopped?.payload.state).toBe('working')
+    })
+
     it('never claims done from a no-lead TeammateIdle park', () => {
       claudeEvent({
         hook_event_name: 'SubagentStart',

src/shared/agent-hook-listener.ts

@@ -2594,8 +2594,16 @@ function buildClaudeChildDrivenStatusPayload(
     })
   }
   if (evidence.removedRow) {
+    // Why: the stop's own inventory can list work this listener never saw start (post-restart);
+    // a running non-teammate task or live shell/cron vetoes done. Teammate-typed entries prove
+    // nothing ("running" even while idle), and full folding here would reap a just-parked
+    // teammate row before its TeammateIdle confirmation arrives — veto only, no reconcile.
+    const inventory = readClaudeBackgroundAgentTasks(hookPayload)
+    const inventoryShowsLiveWork =
+      inventory.tasks.some((task) => task.running && !task.teammate) ||
+      hasActiveClaudeNonAgentBackgroundWork(hookPayload)
     return buildClaudeStatusPayload(state, eventName, '', paneKey, hookPayload, {
-      stateName: 'done',
+      stateName: inventoryShowsLiveWork ? 'working' : 'done',
       updateToolSnapshot: false
     })
   }