fix(async-tasks): auto-wakeup notification not firing when parent session is idle

[randomm]

Bug

When an async task completes, the parent session is NOT automatically woken up to deliver the result. The PM only discovers task completion when explicitly polling via check_task or list_tasks.

Observed Behavior

1. PM dispatches task (async mode)
2. Subagent completes in ~7s
3. PM sits idle for 50+ seconds with no notification
4. User asks 'did the agent finish?'
5. PM calls check_task and discovers it completed

Expected Behavior

When subagent completes, parent session should receive an automatic notification injecting [System: Background tasks completed] into context, triggering the PM to respond.

Root Cause Analysis

enableAutoWakeup() in async-tasks.ts subscribes to BackgroundTaskEvent.Completed on the Bus. When the event fires, triggerWakeup() calls SessionPrompt.prompt() with empty parts — relying on getAndClearCompletedTasks() to inject the completed task notification.

Suspected causes:

1. wakeupInProgress guard blocking re-entry if parent session was still processing
2. hasUndeliveredCompletedTasks(sessionID) filtering by wrong sessionID (child vs parent)
3. Race condition: task completes before enableAutoWakeup subscription is fully registered
4. Bus pub/sub not crossing ACP session boundary correctly

Key Code

• src/session/async-tasks.ts — enableAutoWakeup(), triggerWakeup()
• src/tool/task.ts — calls enableAutoWakeup(ctx.sessionID) before spawning task
• Bus event published with parentSessionID = ctx.sessionID
• Handler filters: event.properties.parentSessionID !== sessionID

Quality Gates

• Reproduce with test
• Fix root cause
• Verify auto-notification fires reliably
• No regression in sync mode

[randomm]

Resolved by two subsequent fixes that landed on dev:

• fix(async-tasks): inject completed tasks in prompt() for auto-wakeup #195 fix(async-tasks): inject completed tasks in prompt() for auto-wakeup — fixed the root cause where completed task results were not being injected into the parent session prompt
• fix(async-tasks): mark task completion injection as synthetic #197 fix(async-tasks): mark task completion injection as synthetic — fixed the follow-on issue where the injected notification was not marked synthetic, causing it to be treated as a real user message

The auto-wakeup system is confirmed working — parent sessions reliably receive [System: Background tasks completed] notifications when subagents complete. Closing as fixed.