## Summary
Wire VAPID web push notifications into the Agents (chat) system so users
get desktop notifications when an agent finishes running.
### Backend
- Add `webpush.Dispatcher` to `chatd.Server` and pass it through from
`coderd.Options.WebPushDispatcher`
- In `processChat()`'s deferred cleanup, dispatch a web push
notification when the chat reaches a terminal state:
- **`waiting`** (success): "Agent has finished running."
- **`error`** (failure): the error message, or "Agent encountered an
error."
- Sub-agent chats (`ParentChatID.Valid`) are skipped to avoid
notification spam from internal delegation
- Gracefully no-ops when the dispatcher is nil (web push disabled)
### Frontend
- New `WebPushButton` component — a bell icon that uses the existing
`useWebpushNotifications` hook
- Returns `null` when the `web-push` experiment is off
- Three states: loading spinner, green bell (subscribed), muted bell-off
(unsubscribed)
- Tooltip + toast feedback on toggle
- Added to both the Agents page empty state top bar and the AgentDetail
top bar
- The Agents page has its own layout (no standard Navbar), so it needs
its own subscribe button
### End-to-end flow
1. User clicks the bell icon on `/agents` → browser subscribes via VAPID
2. User starts an agent chat → chat enters `running` status
3. Agent finishes → `processChat` defer sets status to `waiting`/`error`
→ dispatches web push
4. Browser service worker shows a desktop notification with the chat
title and status
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Co-authored-by: Coder <coder@users.noreply.github.com>
Kyle Carberry
c9ed1e17fc