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/components/views/SettingsView.tsx

@@ -330,6 +330,10 @@ export const SettingsView: React.FC<SettingsViewProps> = ({ onClose, forceMobile
   const isDesktopLocalOrigin = React.useMemo(() => {
     return isDesktopShell() && isDesktopLocalOriginActive();
   }, []);
+  const isMac = React.useMemo(() => {
+    return isDesktopShell() && typeof window !== 'undefined'
+      && (window as unknown as { __OPENCHAMBER_PLATFORM__?: string }).__OPENCHAMBER_PLATFORM__ === 'darwin';
+  }, []);
 
   // keep platform check available for future window chrome tweaks
 
@@ -532,12 +536,12 @@ export const SettingsView: React.FC<SettingsViewProps> = ({ onClose, forceMobile
   const settingsSearchResults = React.useMemo(() => {
     return buildSettingsSearchResults({
       query: settingsSearchQuery,
-      runtimeCtx: { ...runtimeCtx, isDesktopLocalOrigin },
+      runtimeCtx: { ...runtimeCtx, isDesktopLocalOrigin, isMac },
       visiblePageSlugs,
       t,
       getPageTitle,
     });
-  }, [getPageTitle, isDesktopLocalOrigin, runtimeCtx, settingsSearchQuery, t, visiblePageSlugs]);
+  }, [getPageTitle, isDesktopLocalOrigin, isMac, runtimeCtx, settingsSearchQuery, t, visiblePageSlugs]);
 
   const prepareSettingsSearchTarget = React.useCallback((result: SettingsSearchResult): string => {
     if (result.id.startsWith('agents.')) {