feat(desktop): macOS menu bar tray with live session state and mini-chat UX

Add an always-visible macOS status bar (tray) item that surfaces OpenChamber's
live state and acts as a quick launcher, plus a series of related desktop UX
fixes around mini-chat, window routing, notifications and shortcuts.

Tray (new):
- Monochrome template cube glyph that adapts to the menu bar light/dark.
- Icon-driven activity indicator: a smooth, eased, infinite "breathing" fill
  while sessions are busy; a static filled cube when finished sessions are left
  unread; a plain outline when idle. Text counters next to the icon only for
  actionable states (pending approvals, errors).
- Menu lists active sessions (status glyph, branch, unread count) with overflow
  rolled into a submenu; pending permission/question approvals with inline
  Allow once / Allow always / Deny; quick actions (New Session, New Mini Chat,
  Show OpenChamber, Quit). Header shows the active instance name
  ("Local OpenChamber" or the remote host label) for multi-window clarity.
- Session list sourced from the global (cross-project) sessions store, sorted by
  last-updated, independent of which directories are currently open; live
  status/unread/branch merged in from directory sync stores where available.
  Sub-session (multi-run) activity rolls up to the parent row.
- Event-driven updates (global store + directory stores + notifications +
  registry) with a short debounce; polling kept only as a slow safety net.

Tray/window routing:
- Opening a session from the tray targets the surface the user was last on: if a
  mini-chat is active it switches that existing window to the session in place
  (no new window); otherwise the main window (revealed without a reload).
- app.activate (dock click) restores the last-focused/minimized window instead
  of spawning a new main window; only creates one when nothing is left.
- "Open in main window" and tray session-open now create the main window when
  none exists, queuing the session as a pending deep-link so it opens once the
  fresh renderer is ready.

Mini chat:
- New Mini Chat is now a customizable shortcut, exposed in Settings > Shortcuts,
  in the File menu (hint only, renderer owns the binding), and in the tray.
- Themed splash backdrop on window open to remove the white flash / flicker;
  dismissed once content is ready, leaving the content's single cube logo.
- Mini-chat can switch sessions in place via openchamber:open-session.

Notifications:
- The active/selected session only counts as "seen" when the window is focused,
  so turns completing while the app is backgrounded raise an unread marker;
  refocusing the window clears it.

packages/ui/src/App.tsx

@@ -10,6 +10,7 @@ import { ErrorBoundary } from '@/components/ui/ErrorBoundary';
 // useEventStream removed — replaced by SyncProvider + SyncBridge
 import { useMenuActions } from '@/hooks/useMenuActions';
 import { useSessionStatusBootstrap } from '@/hooks/useSessionStatusBootstrap';
+import { useTraySync } from '@/hooks/useTraySync';
 import { useRouter } from '@/hooks/useRouter';
 import { usePushVisibilityBeacon } from '@/hooks/usePushVisibilityBeacon';
 import { useWebNotificationStream } from '@/hooks/useWebNotificationStream';
@@ -17,7 +18,7 @@ import { usePwaInstallPrompt } from '@/hooks/usePwaInstallPrompt';
 import { useWindowTitle } from '@/hooks/useWindowTitle';
 import { useConfigStore } from '@/stores/useConfigStore';
 import { hasModifier } from '@/lib/utils';
-import { isDesktopLocalOriginActive, isDesktopShell, restartDesktopApp } from '@/lib/desktop';
+import { isDesktopLocalOriginActive, isDesktopShell, restartDesktopApp, invokeDesktop } from '@/lib/desktop';
 import {
   getInjectedBootOutcome,
   getBootInjectionStatus,
@@ -29,6 +30,7 @@ import {
 } from '@/lib/desktopBoot';
 import type { RecoveryVariant } from '@/components/onboarding/DesktopConnectionRecovery';
 import { useSessionUIStore } from '@/sync/session-ui-store';
+import { markSessionViewed } from '@/sync/notification-store';
 import { useDirectoryStore } from '@/stores/useDirectoryStore';
 import { useProjectsStore } from '@/stores/useProjectsStore';
 import { opencodeClient } from '@/lib/opencode/client';
@@ -601,6 +603,38 @@ function App({ apis }: AppProps) {
     return () => window.removeEventListener('openchamber:open-session', handler as EventListener);
   }, []);
 
+  // Open a draft Mini Chat window from the native File menu / tray. Uses a
+  // dedicated single-fire event (not the menu-action channel) because draft
+  // mini-chat windows are NOT deduplicated — a double dispatch would open two.
+  React.useEffect(() => {
+    if (typeof window === 'undefined') return;
+    const onOpenMiniChat = () => {
+      const currentDir = useDirectoryStore.getState().currentDirectory;
+      const { activeProjectId, projects } = useProjectsStore.getState();
+      const activeProject = projects.find((p) => p.id === activeProjectId) ?? null;
+      void invokeDesktop('desktop_open_draft_mini_chat_window', {
+        directory: currentDir || activeProject?.path || '',
+        projectId: activeProject?.id ?? null,
+      });
+    };
+    window.addEventListener('openchamber:open-mini-chat', onOpenMiniChat);
+    return () => window.removeEventListener('openchamber:open-mini-chat', onOpenMiniChat);
+  }, []);
+
+  // When the window regains focus, mark the currently-selected session as seen.
+  // Turn-completes that arrive while the app is backgrounded are intentionally
+  // left unseen (see isViewedInCurrentSession); coming back to the window is the
+  // signal that the user has now looked at it, so the marker clears.
+  React.useEffect(() => {
+    if (typeof window === 'undefined') return;
+    const onFocus = () => {
+      const sessionId = useSessionUIStore.getState().currentSessionId;
+      if (sessionId) markSessionViewed(sessionId);
+    };
+    window.addEventListener('focus', onFocus);
+    return () => window.removeEventListener('focus', onFocus);
+  }, []);
+
   React.useEffect(() => {
     if (typeof window === 'undefined') return;
 
@@ -672,6 +706,8 @@ function App({ apis }: AppProps) {
 
   useMenuActions(handleToggleMemoryDebug);
 
+  useTraySync();
+
   useSessionStatusBootstrap({ enabled: embeddedBackgroundWorkEnabled });
 
   React.useEffect(() => {