Separate notification controls for scheduled task runs and normal chat sessions

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

The desktop app has a single notification category, "Task complete", and it covers two different events: a scheduled task finishing a run, and Claude finishing a reply in a chat I am having. Its only options are Banners and Off.

I run ten recurring scheduled tasks, one of them hourly. That is roughly thirty "Scheduled task completed" banners a day, none of which I need, because every task writes its output where I already look. What I do want is the banner when Claude finishes a reply in a session I started, because that is the moment I am actually waiting.

Today those two share one switch. Turning "Task complete" off silences the notification I rely on; leaving it on costs me thirty interruptions a day.

The per-task `notifyOnCompletion` option does not help here: it controls whether a chat session is woken with a message, which is a separate mechanism from the OS banner.

### Proposed Solution

Split "Task complete" into two rows in Settings > Notifications, each keeping the existing level control:

- **Task complete** - Claude finished and is waiting for your input, for sessions I started.
- **Scheduled task finished** - a scheduled task completed or failed.

For the scheduled-task row, three levels would be better than two: Off / Only on failure / All runs. "Only on failure" is what someone running unattended jobs actually wants. At the moment a task that quietly stops running looks exactly like one that succeeds, because both produce nothing I would notice.

A per-task override in the task's own settings would be ideal, so the hourly job can be silent while the weekly one stays loud, but the two global rows would already solve the problem.

### Alternative Solutions

- Setting `notifyOnCompletion: false` on every scheduled task. No effect on the OS banner; it governs a different path.
- Turning the whole "Task complete" category off. Silences the chat completion banner I want to keep.
- Moving the noisy jobs out of the app into Windows Task Scheduler. Works, but loses the connectors and the artifact surface, and it is a lot of engineering to avoid a notification.

### Priority

Medium - Would be very helpful

### Feature Category

Documentation

### Use Case Example

Between 08:00 and 23:00 my scheduled jobs fire around thirty completion banners: an hourly dashboard sync, a sampler every four hours, a daily digest, a morning summary and several weekly chases.

In the same hours I am usually in a chat doing real work. I minimise the window while Claude thinks, and I rely on the "Claude finished" banner to tell me it is done.

So my day looks like this:

1. I set a long-running request going in a chat and switch to something else.
2. Three scheduled tasks finish in the meantime and each throws a banner I do not need.
3. The banner I do need, the one for my own chat, arrives among them and I miss it.
4. I go to turn the noise off and find that the only switch also removes step 3.

I currently keep the noise, because losing the chat notification costs me more than thirty banners annoy me.

### Additional Context

Claude desktop 1.46388.4, Windows 11.

Where the two events currently meet, as far as I can tell from the app bundle: the scheduled-task banner is emitted on a `scheduledTaskRunFinished` event and gated only by the "idle" banner level plus a check for whether I am currently viewing that session. Chat completion banners are gated by the same "idle" level, which is why one switch controls both.

The Settings UI exposes three notification categories: Permission requests, Questions, and Task complete. The first two offer Off / Badge only / Banners; Task complete offers only Off / Banners, so there is not even a badge-only middle ground for this one.

This is a desktop app request rather than a CLI one; I filed it here because this repository appears to be where product feedback for Claude products is collected. Happy to move it if there is a better place.

No repository file or test is named; begin by locating the desktop Settings > Notifications implementation and the notification handling for scheduledTaskRunFinished and chat completion. Compare how both events are gated by the existing idle level, then define the separate controls and failure-only behavior before identifying appropriate tests. Done means the two event types can be configured independently without changing notifyOnCompletion behavior.

Rédigé par le modèle d'indexation à partir du texte de l'issue.