Add batch still arrows, hide output only on tap, and cut studio lag.

Co-authored-by: Cursor <cursoragent@cursor.com>

components/AppHeader.vue

@@ -1,5 +1,5 @@
 <template>
-  <header class="sticky top-0 z-20 border-b border-white/5 bg-zinc-950/70 backdrop-blur-xl">
+  <header class="sticky top-0 z-20 border-b border-white/5 bg-zinc-950/90 sm:bg-zinc-950/80 sm:backdrop-blur-md">
     <div
       class="mx-auto flex items-center justify-between px-4 py-4 sm:px-6"
       :class="wide ? 'max-w-[90rem]' : 'max-w-7xl'"
@@ -30,7 +30,7 @@
         </div>
         <div
           v-if="menuOpen"
-          class="absolute left-0 top-full z-30 mt-2 w-52 rounded-2xl border border-white/10 bg-zinc-950/95 p-1 shadow-xl shadow-black/40 backdrop-blur-xl"
+          class="absolute left-0 top-full z-30 mt-2 w-52 rounded-2xl border border-white/10 bg-zinc-950/95 p-1 shadow-xl shadow-black/40"
           role="menu"
           @click.stop
         >
@@ -285,7 +285,7 @@ onMounted(async () => {
   healthTimer = setInterval(() => {
     if (typeof document !== 'undefined' && document.hidden) return
     void pollHealth()
-  }, 5000)
+  }, 15000)
 })
 
 onBeforeUnmount(() => {