Remove duplicate MelodyMuse brand row in InputPanel

The home page header already shows a small equalizer + 'MelodyMuse'
wordmark. Having a second brand row inside the InputPanel was
redundant and pushed the textarea down. Removed it; the form now
starts directly with the 'Music idea' label. Bumped the textarea
rows from 4 to 5 to fill the freed space.

Also added: the server-status check on the home page now re-runs
every 30s, so the 'Server offline' hint in the header stays current
without a manual refresh.

src/pages/HomePage.tsx

@@ -96,18 +96,24 @@ export function HomePage() {
     return () => window.clearTimeout(id);
   }, [input]);
 
-  // Check the server on mount. If unreachable, surface a quiet header hint.
+  // Check the server on mount and re-check periodically so the header
+  // "Server offline" hint stays current without a manual refresh.
   useEffect(() => {
-    const ctrl = new AbortController();
-    (async () => {
+    let cancelled = false;
+    const check = async () => {
       try {
-        const s = await getServerStatus(ctrl.signal);
-        setServerOk(Boolean(s.ok));
+        const s = await getServerStatus();
+        if (!cancelled) setServerOk(Boolean(s.ok));
       } catch {
-        setServerOk(false);
+        if (!cancelled) setServerOk(false);
       }
-    })();
-    return () => ctrl.abort();
+    };
+    check();
+    const id = window.setInterval(check, 30_000);
+    return () => {
+      cancelled = true;
+      window.clearInterval(id);
+    };
   }, []);
 
   // Clean up any in-flight request on unmount.