Desktop: Pulse @mentions do not notify or badge while app is unfocused

**Describe the bug**

Pulse `@mentions` do not produce a native desktop notification or a Buzz Home/Mention badge while the Buzz window is open but unfocused.

The relay accepts and indexes the kind:1 event with the recipient's `p` tag correctly. The desktop client also has Desktop alerts, Home badge, and the `mention` alert category enabled. However, the Home feed is not refreshed while the app is unfocused, so the notification pipeline never sees the mention.

This appears to be a notification reliability regression from #5490. That PR intentionally changed `useHomeFeedQuery()` from a normal 30-second interval to `useFocusedRefetchInterval(...)`, pausing network refetches on blur. Pulse mentions are feed-driven rather than delivered through the real-time channel notification path, so they are now silenced whenever the user works in another app.

**Steps to reproduce**

1. In Buzz Desktop, enable:
- Desktop alerts
- Home badge
- Mention alerts
2. Keep Buzz running and connected, then focus another macOS app. Do not quit Buzz.
3. From another Buzz identity, publish a Pulse note (kind:1) with a valid `p` tag for the signed-in user.
4. Wait longer than the Home feed's 30-second polling interval.
5. Observe that:
- no macOS notification appears;
- no Buzz Home/Mention badge appears;
- the mention event is not added to the client's `buzz-home-feed-seen` state while Buzz remains unfocused.

**Expected behavior**

A valid Pulse mention should notify the user while Buzz is running but unfocused, just like other notification-bearing events. At minimum, the Home/Mention badge should update; when desktop alerts are enabled, a native macOS notification should also appear.

The fix should preserve #5490's CPU improvements. Options include keeping only the notification-bearing mentions query active while unfocused, or delivering kind:1 `p`-tag mentions through a real-time WebSocket notification path instead of relying on foreground-only Home feed polling.

**Version and platform**

- Buzz version: 0.5.17
- OS: macOS 26.5.1 (25F80), Apple Silicon

**Logs / additional context**

Controlled live reproduction:

- Buzz Desktop process remained running.
- Relay returned HTTP 200 and stored the kind:1 event.
- Server-side `event_mentions` indexed exactly the intended recipient `p` tag.
- Client settings confirmed `desktopEnabled: true`, `homeBadgeEnabled: true`, and `slotAlertsEnabled.mention: true`.
- After more than 30 seconds with Buzz unfocused, the event ID was still absent from the client's `buzz-home-feed-seen` local state.
- Test events were deleted after verification.

Relevant code/history:

- #5490 changed `desktop/src/features/home/hooks.ts` to use `useFocusedRefetchInterval(connected ? 30_000 : false)` and explicitly documents that network query polling pauses on blur.
- `desktop/src/features/notifications/use-feed-desktop-notifications.ts` emits mention notifications only when the Home feed query returns a new eligible item.
- The reminder-notification reliability concern was explicitly handled during #5490 review, but feed-based Pulse mentions were not covered by an equivalent exception or regression test.