feat(desktop): add macOS dock badge for chats with unseen activity

Show a count of chats (root sessions) with unseen activity on the macOS
dock icon. The count is computed in the existing tray snapshot (full
cross-project list, not the capped tray view; a subtask's unseen rolls up
to its root only when subtask notifications are enabled) and pushed to the
main process over the existing desktop_tray_update IPC, which calls
app.setBadgeCount (0 clears it). The badge clears as sessions are marked
seen on window focus.

Add a Dock badge toggle in Appearance settings (default on, persisted,
darwin desktop only), localized across all dictionaries, with a matching
settings-search entry whose availability mirrors the render guard exactly.

packages/ui/src/lib/i18n/messages/ko.settings.ts

@@ -1572,6 +1572,8 @@ export const settingsDict = {
   'settings.openchamber.visual.actions.reloadThemes': '테마 다시 로드',
   'settings.openchamber.visual.field.macVibrancy': '창 투명도',
   'settings.openchamber.visual.field.macVibrancyHint': '사이드바 뒤에 macOS 기본 블러(vibrancy)를 사용합니다. 완전히 불투명한 표면을 원하면 끄세요.',
+  'settings.openchamber.visual.field.dockBadge': 'Dock 배지',
+  'settings.openchamber.visual.field.dockBadgeHint': '확인하지 않은 활동이 있는 채팅 수를 macOS Dock 아이콘에 표시합니다.',
   'settings.openchamber.visual.actions.saveAndRestart': '저장 후 재시작',
   'settings.openchamber.visual.actions.restarting': '재시작 중…',
   'settings.openchamber.visual.actions.reloadingThemes': '테마 다시 로드 중...',