refactor(background-agent): wire ParentWakeNotifier into BackgroundManager

Replace the inlined parent-wake coalescing logic in manager.ts with delegation to the ParentWakeNotifier extracted in c1ccf8d09. The four timer Maps and the related methods now live in their own module with a narrow public API, while BackgroundManager retains the wiring point and the enqueue-callback bridge.

Closes HIGH-9 (step 2: integration)

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/features/background-agent/manager.test.ts

@@ -233,11 +233,15 @@ function getPendingNotifications(manager: BackgroundManager): Map<string, string
 }
 
 function getPendingParentWakes(manager: BackgroundManager): Map<string, PendingParentWakeForTest> {
-  return (cast<{ pendingParentWakes: Map<string, PendingParentWakeForTest> }>(manager)).pendingParentWakes
+  return (cast<{
+    parentWakeNotifier: { getPendingParentWakes: () => Map<string, PendingParentWakeForTest> }
+  }>(manager)).parentWakeNotifier.getPendingParentWakes()
 }
 
 function getDispatchedParentWakes(manager: BackgroundManager): Map<string, PendingParentWakeForTest> {
-  return (cast<{ dispatchedParentWakes: Map<string, PendingParentWakeForTest> }>(manager)).dispatchedParentWakes
+  return (cast<{
+    parentWakeNotifier: { getDispatchedParentWakes: () => Map<string, PendingParentWakeForTest> }
+  }>(manager)).parentWakeNotifier.getDispatchedParentWakes()
 }
 
 function getCompletionTimers(manager: BackgroundManager): Map<string, ReturnType<typeof setTimeout>> {