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/sync/sync-context.tsx

@@ -387,9 +387,21 @@ export function setExternallyViewedSession(directory: string, sessionId: string,
   externallyViewedSessions.set(key, Date.now() + EXTERNAL_VIEW_TTL_MS)
 }
 
+// The window must actually be focused for the active session to count as
+// "seen": if the app is minimized or in the background, a turn finishing in the
+// currently-selected session should still raise an unseen marker (in the tray
+// and in-app), since the user isn't looking at it.
+function isWindowFocused(): boolean {
+  return typeof document !== "undefined" && document.hasFocus()
+}
+
 function isViewedInCurrentSession(directory: string, sessionId?: string): boolean {
   if (!sessionId) return false
-  if (_activeDirectory && _activeSession && directory === _activeDirectory && sessionId === _activeSession) return true
+  if (
+    _activeDirectory && _activeSession
+    && directory === _activeDirectory && sessionId === _activeSession
+    && isWindowFocused()
+  ) return true
   pruneExternallyViewedSessions()
   return externallyViewedSessions.has(viewedSessionKey(directory, sessionId))
 }