fix(background-agent): treat non-active session statuses as terminal to prevent parent session hang

Previously, pollRunningTasks() and checkAndInterruptStaleTasks() treated
any non-"idle" session status as "still running", which caused tasks with
terminal statuses like "interrupted" to be skipped indefinitely — both
for completion detection AND stale timeout. This made the parent session
hang forever waiting for an ALL COMPLETE notification that never came.

Extract isActiveSessionStatus() and isTerminalSessionStatus() that
classify session statuses explicitly. Only known active statuses
("busy", "retry", "running") protect tasks from completion/stale checks.
Known terminal statuses ("interrupted") trigger immediate completion.
Unknown statuses fall through to the standard idle/gone path with output
validation as a conservative default.

Introduced by: a0c93816 (2026-02-14), dc370f7f (2026-03-08)

src/features/background-agent/task-poller.test.ts

@@ -417,6 +417,56 @@ describe("checkAndInterruptStaleTasks", () => {
     expect(task.status).toBe("cancelled")
     expect(onTaskInterrupted).toHaveBeenCalledWith(task)
   })
+
+  it('should NOT protect task when session has terminal non-idle status like "interrupted"', async () => {
+    //#given — lastUpdate is 5min old, session is "interrupted" (terminal, not active)
+    const task = createRunningTask({
+      startedAt: new Date(Date.now() - 300_000),
+      progress: {
+        toolCalls: 2,
+        lastUpdate: new Date(Date.now() - 300_000),
+      },
+    })
+
+    //#when — session status is "interrupted" (terminal)
+    await checkAndInterruptStaleTasks({
+      tasks: [task],
+      client: mockClient as never,
+      config: { staleTimeoutMs: 180_000 },
+      concurrencyManager: mockConcurrencyManager as never,
+      notifyParentSession: mockNotify,
+      sessionStatuses: { "ses-1": { type: "interrupted" } },
+    })
+
+    //#then — terminal statuses should not protect from stale timeout
+    expect(task.status).toBe("cancelled")
+    expect(task.error).toContain("Stale timeout")
+  })
+
+  it('should NOT protect task when session has unknown status type', async () => {
+    //#given — lastUpdate is 5min old, session has an unknown status
+    const task = createRunningTask({
+      startedAt: new Date(Date.now() - 300_000),
+      progress: {
+        toolCalls: 2,
+        lastUpdate: new Date(Date.now() - 300_000),
+      },
+    })
+
+    //#when — session has unknown status type
+    await checkAndInterruptStaleTasks({
+      tasks: [task],
+      client: mockClient as never,
+      config: { staleTimeoutMs: 180_000 },
+      concurrencyManager: mockConcurrencyManager as never,
+      notifyParentSession: mockNotify,
+      sessionStatuses: { "ses-1": { type: "some-weird-status" } },
+    })
+
+    //#then — unknown statuses should not protect from stale timeout
+    expect(task.status).toBe("cancelled")
+    expect(task.error).toContain("Stale timeout")
+  })
 })
 
 describe("pruneStaleTasksAndNotifications", () => {