Extracts the parent-wake coalescing logic (pending/dispatched wake maps,
timers, notification reply assembly) from manager.ts into a standalone
ParentWakeNotifier class. Takes dependency-injected client, directory,
and an enqueueNotificationForParent callback, so the manager can delegate
parent-wake state to a narrow API.
This commit only introduces the new module; wiring manager.ts to use it
is a follow-up commit so the refactor stays atomic (HIGH-9 step 1 of 2).
Closes HIGH-9 (step 1: extraction)
Refs HIGH-9 (step 2: manager.ts integration deferred until verification)
Co-authored-by: manager-extract (deep / gpt-5.3-codex high)
YeonGyu-Kim