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 />

apps/web/src/components/ui/ResourceBar.tsx

@@ -6,13 +6,29 @@ interface ResourceBarProps {
   prestigeCount: number;
   profileUrl: string;
   onEditProfile: () => void;
+  lastSavedAt: number | null;
+  isSyncing: boolean;
+  onForceSync: () => Promise<void>;
 }
 
+const formatRelativeTime = (timestamp: number): string => {
+  const seconds = Math.floor((Date.now() - timestamp) / 1000);
+  if (seconds < 10) return "just now";
+  if (seconds < 60) return `${seconds}s ago`;
+  const minutes = Math.floor(seconds / 60);
+  if (minutes < 60) return `${minutes}m ago`;
+  const hours = Math.floor(minutes / 60);
+  return `${hours}h ago`;
+};
+
 export const ResourceBar = ({
   resources,
   prestigeCount,
   profileUrl,
   onEditProfile,
+  lastSavedAt,
+  isSyncing,
+  onForceSync,
 }: ResourceBarProps): React.JSX.Element => (
   <header className="resource-bar">
     <div className="resource">
@@ -41,6 +57,20 @@ export const ResourceBar = ({
       </div>
     )}
     <div className="profile-buttons">
+      {lastSavedAt !== null && (
+        <span className="save-status" title={new Date(lastSavedAt).toLocaleString()}>
+          ☁️ {formatRelativeTime(lastSavedAt)}
+        </span>
+      )}
+      <button
+        className="force-save-button"
+        disabled={isSyncing}
+        onClick={onForceSync}
+        title="Force cloud save"
+        type="button"
+      >
+        {isSyncing ? "⏳" : "💾"}
+      </button>
       <a
         className="profile-link-button"
         href={profileUrl}