Extends useTauriNotificationBadge to also invoke set_tray_unread (mirror the
unread-mention state onto the tray icon, visible when minimized) and flash_window
(flash the taskbar button when new mentions arrive while the window is unfocused).
No-op outside Tauri.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Adds a Tauri command (set_badge_count) that draws a red circle badge
with a highlight count onto the Windows taskbar button overlay icon,
matching Discord's behavior. Badge shows @mention/highlight count only
(not total messages), clears to zero when all highlights are read.
Frontend: useTauriNotificationBadge hook reads roomToUnreadAtom and
calls set_badge_count via window.__TAURI_INTERNALS__.invoke whenever
the unread map changes. No-ops silently in the browser (non-Tauri).
Mounted as TauriEffects inside JotaiProvider in App.tsx.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
jared