fix(background-agent): defer parent wake during active turns

src/features/background-agent/parent-wake-active-turn-event.test.ts

@@ -108,7 +108,7 @@ async function flushPendingParentWakeForTest(manager: BackgroundManager, session
 }
 
 describe("BackgroundManager parent wake active turn events", () => {
-  test("#when background task completes during active parent turn #then parent gets same-turn no-reply reminder", async () => {
+  test("#when background task completes during active parent turn #then parent wake stays deferred", async () => {
     // given
     const sessionStatuses: Record<string, { type: string }> = {
       "parent-1": { type: "busy" },
@@ -129,9 +129,57 @@ describe("BackgroundManager parent wake active turn events", () => {
     await notifyParentSessionForTest(manager, task)
     await flushPendingParentWakeForTest(manager, "parent-1")
 
+    // then
+    expect(promptAsyncCalls).toHaveLength(0)
+    expect(getPendingParentWakes(manager).has("parent-1")).toBe(true)
+  })
+
+  test("#when duplicate background completions overlap an active parent turn #then one coalesced wake dispatches after idle", async () => {
+    // given
+    const sessionStatuses: Record<string, { type: string }> = {
+      "parent-1": { type: "busy" },
+    }
+    const { manager, promptAsyncCalls } = createManager(sessionStatuses)
+    managerUnderTest = manager
+    const taskA = createTask({
+      id: "task-a",
+      parentSessionId: "parent-1",
+      description: "task A",
+      status: "completed",
+      completedAt: new Date("2026-05-20T14:19:14.625Z"),
+    })
+    const taskB = createTask({
+      id: "task-b",
+      parentSessionId: "parent-1",
+      description: "task B",
+      status: "completed",
+      completedAt: new Date("2026-05-20T14:19:15.625Z"),
+    })
+    getTasks(manager).set(taskA.id, taskA)
+    getTasks(manager).set(taskB.id, taskB)
+    getPendingByParent(manager).set(taskA.parentSessionId, new Set([taskA.id, taskB.id]))
+
+    // when
+    await notifyParentSessionForTest(manager, taskA)
+    await notifyParentSessionForTest(manager, taskB)
+    await Promise.all([
+      flushPendingParentWakeForTest(manager, "parent-1"),
+      flushPendingParentWakeForTest(manager, "parent-1"),
+    ])
+
+    // then
+    expect(promptAsyncCalls).toHaveLength(0)
+    expect(getPendingParentWakes(manager).has("parent-1")).toBe(true)
+
+    // when
+    sessionStatuses["parent-1"] = { type: "idle" }
+    await Promise.all([
+      flushPendingParentWakeForTest(manager, "parent-1"),
+      flushPendingParentWakeForTest(manager, "parent-1"),
+    ])
+
     // then
     expect(promptAsyncCalls).toHaveLength(1)
-    expect(promptAsyncCalls[0]?.body.noReply).toBe(true)
     expect(JSON.stringify(promptAsyncCalls[0]?.body.parts)).toContain("ALL BACKGROUND TASKS COMPLETE")
     expect(getPendingParentWakes(manager).has("parent-1")).toBe(false)
   })