Mute notifications for a single thread

[BOTKooper]

Problem

I run some threads that finish on a schedule, such as an AI review bot set up through scheduled tasks. Every run sends a "Thread completed" alert to every device: a system notification and sound on desktop, a toast in the app, and a push on my phone. The only way to silence them is to turn notifications off everywhere, which also hides the threads I do care about.

Proposal

Let a user mute one thread's notifications, on every device at once:

• Where: Mute notifications / Unmute notifications in the thread menu (sidebar right-click and chat header on web and desktop, long-press menu on mobile). Agents can also do it through t3_thread_organize, so a scheduled task can mute its own thread.
• What it silences: system notifications, sounds and in-app toasts on web and desktop, plus mobile push and Live Activities.
• What stays: the thread still shows its status in the sidebar. Only alerts are withheld.

Because the mute has to follow the thread across devices, it would be stored on the thread on the server (a mutedAt timestamp set by a thread.mute.set command), not as a per-device setting. Muting isn't activity, so it wouldn't reorder the list or affect auto-settle. The relay publisher would treat a muted thread like an archived one, so mobile gets nothing.

Prototype

I have a working implementation with tests and a demo video in draft PR #16800. A cron thread shows a "Thread completed" toast every minute; after Mute notifications, the toasts stop.

Is per-thread mute a direction you'd accept, and is a server-side flag on the thread the right scope?