feat(demo): header countdown switches to reset timer when questions exhausted

When a user hits the 10-question limit, the header countdown flips from
'0 questions left' to a live 'resets in HH:MM:SS' ticker counting to
midnight UTC. Clears automatically when the session resets.

src/js/chat-widget.el

@@ -76,17 +76,59 @@ fn main() -> Void {
     saveSession(session);
   }
   var msgCount = session.count || 0;
+  var _headerResetInterval = null;
+
+  function _nextMidnightUTC() {
+    var now = new Date();
+    var midnight = new Date(Date.UTC(now.getUTCFullYear(), now.getUTCMonth(), now.getUTCDate() + 1));
+    return Math.floor(midnight.getTime() / 1000);
+  }
+
+  function _startHeaderResetTimer() {
+    var el = document.getElementById('neuron-demo-countdown');
+    if (!el) return;
+    if (_headerResetInterval) return; // already ticking
+    var resetAt = _nextMidnightUTC();
+    function _tick() {
+      var secsLeft = Math.max(0, resetAt - Math.floor(Date.now() / 1000));
+      var hh = Math.floor(secsLeft / 3600);
+      var mm = Math.floor((secsLeft % 3600) / 60);
+      var ss = secsLeft % 60;
+      var pad = function(n) { return n < 10 ? '0' + n : '' + n; };
+      var ts = hh + ':' + pad(mm) + ':' + pad(ss);
+      var el2 = document.getElementById('neuron-demo-countdown');
+      if (!el2) { clearInterval(_headerResetInterval); _headerResetInterval = null; return; }
+      el2.textContent = 'resets in ' + ts;
+      el2.style.color = 'rgba(255,255,255,0.65)';
+      el2.style.fontWeight = '600';
+      if (secsLeft <= 0) {
+        clearInterval(_headerResetInterval);
+        _headerResetInterval = null;
+        el2.textContent = '10 questions left';
+        el2.style.color = '#ffffff';
+        el2.style.fontWeight = '700';
+      }
+    }
+    _tick();
+    _headerResetInterval = setInterval(_tick, 1000);
+  }
 
   function updateCountdown() {
     var el = document.getElementById('neuron-demo-countdown');
     if (!el) return;
     var remaining = MAX - msgCount;
-    el.textContent   = remaining + ' question' + (remaining === 1 ? '' : 's') + ' left';
-    el.style.color   = '#ffffff';
-    el.style.fontWeight = '700';
+    if (remaining <= 0) {
+      _startHeaderResetTimer();
+    } else {
+      if (_headerResetInterval) { clearInterval(_headerResetInterval); _headerResetInterval = null; }
+      el.textContent   = remaining + ' question' + (remaining === 1 ? '' : 's') + ' left';
+      el.style.color   = '#ffffff';
+      el.style.fontWeight = '700';
+    }
   }
 
   window.neuronDemoReset = function() {
+    if (_headerResetInterval) { clearInterval(_headerResetInterval); _headerResetInterval = null; }
     clearSession();
     session  = { messages: [], count: 0, context: '' };
     msgCount = 0;