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/ja.settings.ts

@@ -1606,6 +1606,8 @@ export const settingsDict = {
   'settings.openchamber.visual.actions.reloadingThemes': 'テーマを再読み込み中...',
   'settings.openchamber.visual.field.macVibrancy': 'ウィンドウ透過',
   'settings.openchamber.visual.field.macVibrancyHint': 'サイドバーの背後に macOS ネイティブのぼかし（Vibrancy）を使用します。完全に不透明なサーフェスにする場合はオフにします。',
+  'settings.openchamber.visual.field.dockBadge': 'Dock バッジ',
+  'settings.openchamber.visual.field.dockBadgeHint': '未読のアクティビティがあるチャットの数を macOS の Dock アイコンに表示します。',
   'settings.openchamber.visual.actions.saveAndRestart': '保存して再起動',
   'settings.openchamber.visual.actions.restarting': '再起動中...',
   'settings.openchamber.visual.field.themeImportInfoAria': 'テーマインポート情報',