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/manager.polling.test.ts

@@ -153,4 +153,42 @@ describe("BackgroundManager pollRunningTasks", () => {
       expect(task.status).toBe("running")
     })
   })
+
+  describe("#given a running task whose session has terminal non-idle status", () => {
+    test('#when session status is "interrupted" #then completes the task', async () => {
+      //#given
+      const manager = createManagerWithClient({
+        status: async () => ({ data: { "ses-interrupted": { type: "interrupted" } } }),
+      })
+      const task = createRunningTask("ses-interrupted")
+      injectTask(manager, task)
+
+      //#when
+      const poll = (manager as unknown as { pollRunningTasks: () => Promise<void> }).pollRunningTasks
+      await poll.call(manager)
+      manager.shutdown()
+
+      //#then
+      expect(task.status).toBe("completed")
+      expect(task.completedAt).toBeDefined()
+    })
+
+    test('#when session status is an unknown type #then completes the task', async () => {
+      //#given
+      const manager = createManagerWithClient({
+        status: async () => ({ data: { "ses-unknown": { type: "some-weird-status" } } }),
+      })
+      const task = createRunningTask("ses-unknown")
+      injectTask(manager, task)
+
+      //#when
+      const poll = (manager as unknown as { pollRunningTasks: () => Promise<void> }).pollRunningTasks
+      await poll.call(manager)
+      manager.shutdown()
+
+      //#then
+      expect(task.status).toBe("completed")
+      expect(task.completedAt).toBeDefined()
+    })
+  })
 })