fix(agent-status): reap only unbacked claims from an empty stop inventory

Review finding round 11: the complete-empty fold cleared live-tracked
rows, so a delayed stale stop's empty list could retire a newer live
start — the uncorrelated-retirement race again. The empty inventory now
reaps only restored/inventory-derived claims not backed by live
lifecycle events.

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

@@ -3350,6 +3350,28 @@ describe('shared agent-hook-listener', () => {
       expect(stopped?.payload.subagents).toBeUndefined()
     })
 
+    it('keeps a newer live start alive through a delayed stale stop with an empty inventory', () => {
+      claudeEvent({
+        hook_event_name: 'SubagentStart',
+        agent_id: 'a-old',
+        agent_type: 'general-purpose'
+      })
+      claudeEvent({
+        hook_event_name: 'SubagentStart',
+        agent_id: 'a-new',
+        agent_type: 'general-purpose'
+      })
+      // Why: a-old's delayed stop reports the empty inventory captured before
+      // a-new existed; clearing a-new from it would retire newer live work.
+      const staleStop = claudeEvent({
+        hook_event_name: 'SubagentStop',
+        agent_id: 'a-old',
+        background_tasks: []
+      })
+      expect(staleStop?.payload.state).toBe('working')
+      expect(staleStop?.payload.subagents).toEqual([expect.objectContaining({ id: 'a-new' })])
+    })
+
     it('clears restored phantom rows when a no-lead stop carries a complete empty inventory', () => {
       seedClaudeSubagentRosterFromSnapshots(state, PANE_KEY, [
         { id: 'a1', state: 'working', startedAt: 1, agentType: 'general-purpose' },

src/shared/agent-hook-listener.ts

@@ -2471,7 +2471,16 @@ function normalizeClaudeSubagentLifecycleEvent(
       // Additive only — a complete-inventory reap here would kill a just-parked teammate row
       // before its TeammateIdle confirmation arrives.
       const inventory = readClaudeBackgroundAgentTasks(hookPayload)
-      if (
+      if (inventory.present && inventory.tasks.length === 0 && roster) {
+        // Why: an empty complete inventory reaps only claims not backed by live lifecycle events
+        // (restored/inventory-derived phantoms). A delayed stale stop's empty list must not clear
+        // a newer live start's row — that is the uncorrelated-retirement race again.
+        for (const [id, tracked] of roster) {
+          if (tracked.restoredFromSnapshot || tracked.backgroundTasksAuthoritative) {
+            roster.delete(id)
+          }
+        }
+      } else if (
         inventory.present &&
         (roster ||
           inventory.tasks.some(
@@ -2484,11 +2493,9 @@ function normalizeClaudeSubagentLifecycleEvent(
           getOrCreateClaudeSubagentRoster(state, paneKey),
           inventory.tasks,
           Date.now(),
-          // Why: an empty inventory is complete by construction and proves nothing is left
-          // alive (lead-path rule), clearing restored phantoms; a non-empty one folds
-          // additively — its reap would kill a just-parked teammate row before its
-          // TeammateIdle confirmation arrives.
-          { inventoryComplete: inventory.tasks.length === 0 }
+          // Why: additive only — a complete-inventory reap here would kill a just-parked
+          // teammate row before its TeammateIdle confirmation arrives.
+          { inventoryComplete: false }
         )
       }
       // Why: a blocked child that dies without another tool event would pin its permission/question wait on the pane forever — nothing else references that agent again.