feat: add cloud save timestamp and force sync button

Shows a relative time label (e.g. "☁️ 2m ago") in the resource bar
seeded from the server on load and updated after every auto-save or
manual save. A 💾 button lets players trigger an immediate cloud save
outside the 30-second auto-save cycle, with a ⏳ spinner and disabled
state while the request is in-flight.

apps/web/src/components/game/GameLayout.tsx

@@ -27,7 +27,7 @@ const TABS: { id: Tab; label: string }[] = [
 ];
 
 export const GameLayout = (): React.JSX.Element => {
-  const { state, isLoading, error, battleResult, dismissBattle } = useGame();
+  const { state, isLoading, error, battleResult, dismissBattle, lastSavedAt, isSyncing, forceSync } = useGame();
   const [activeTab, setActiveTab] = useState<Tab>("adventurers");
   const [editingProfile, setEditingProfile] = useState(false);
 
@@ -58,6 +58,9 @@ export const GameLayout = (): React.JSX.Element => {
         prestigeCount={state.prestige.count}
         profileUrl={profileUrl}
         onEditProfile={() => { setEditingProfile(true); }}
+        lastSavedAt={lastSavedAt}
+        isSyncing={isSyncing}
+        onForceSync={forceSync}
       />
       <OfflineModal />
       <AchievementToast />