fix: restore live/offline indicator dropped during Header extraction

The wsConnected prop was destructured but unused. This restores the
live/offline status pill next to the page title, matching the original
Header function design and consuming the prop properly.

client/src/components/run/LaneConsolePane.tsx

@@ -54,6 +54,7 @@ export function LaneConsolePane({
 }: LaneConsolePaneProps) {
   const { t } = useTranslation("run");
   const { t: tLanes } = useTranslation("lanes");
+  const { t: tCommon } = useTranslation("common");
 
   const [prompt, setPrompt] = useState("");
   const [model, setModel] = useState("");
@@ -303,7 +304,20 @@ export function LaneConsolePane({
           <Play className="w-4.5 h-4.5 text-accent" />
         </div>
         <div className="min-w-0 flex-1">
-          <h1 className="text-lg font-semibold text-fg-primary">{t("title")}</h1>
+          <div className="flex items-center gap-2">
+            <h1 className="text-lg font-semibold text-fg-primary">{t("title")}</h1>
+            {wsConnected ? (
+              <span className="flex items-center gap-1.5 text-[11px] text-status-success bg-status-success/10 border border-status-success/20 px-2 py-0.5 rounded-full">
+                <span className="w-1.5 h-1.5 rounded-full bg-status-success animate-pulse-dot" />
+                {tCommon("live")}
+              </span>
+            ) : (
+              <span className="flex items-center gap-1.5 text-[11px] text-fg-secondary bg-surface-4/10 border border-border-light/20 px-2 py-0.5 rounded-full">
+                <span className="w-1.5 h-1.5 rounded-full bg-surface-4" />
+                {tCommon("offline")}
+              </span>
+            )}
+          </div>
           <p className="text-xs text-fg-muted max-w-3xl">{t("subtitle")}</p>
         </div>
         <ActiveRunsSwitcher