feat(audience-sample): respect Android safe area in sample app UI (SDK-314)

Apply Screen.safeArea insets as root VisualElement padding so content
is never obscured by the status bar, notch, or navigation bar on Android.
Padding is updated every frame when the safe area rect changes (startup
and orientation changes); a too-early call before layout is settled
retries automatically the following frame.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: nattb8

examples/audience/Assets/SampleApp/Scripts/AudienceSample.UI.cs

@@ -84,6 +84,9 @@ private static readonly (string TabId, string PanelId)[] Tabs =
 
 #pragma warning restore 8618
 
+        // Tracks the last applied safe area so Update only re-applies on change.
+        private Rect _lastSafeArea;
+
         // ---- UI lifecycle (single entry point called from main's Awake) ----
 
         // Full UI lifecycle: thread capture, document load, binding, callbacks,
@@ -113,6 +116,15 @@ private void InitializeUi()
             _root.schedule.Execute(RefreshStatusBar).Every(StatusPollIntervalMs);
         }
 
+        // Re-apply safe-area padding whenever Screen.safeArea changes (startup,
+        // orientation flip, multi-window resize). Runs every frame but exits
+        // immediately when nothing has changed.
+        private void Update()
+        {
+            if (Screen.safeArea != _lastSafeArea)
+                ApplySafeArea();
+        }
+
         // ---- UI document load ----
 
         // Loads the UXML/USS resources and clones the tree into the panel
@@ -444,6 +456,32 @@ void Update()
             _root.schedule.Execute(Update).StartingIn(0);
         }
 
+        // Converts Screen.safeArea insets (screen-space pixels) to root
+        // VisualElement padding (panel layout units). Called by Update() on
+        // every frame where the safe area rect changes — typically once on
+        // startup and once per orientation change.
+        //
+        // _lastSafeArea is updated only on success so that a too-early call
+        // (layout not yet settled) retries automatically next frame.
+        private void ApplySafeArea()
+        {
+            if (_root == null) return;
+            var w = _root.layout.width;
+            var h = _root.layout.height;
+            if (float.IsNaN(w) || w <= 0f || float.IsNaN(h) || h <= 0f) return;
+
+            var safe   = Screen.safeArea;
+            var scaleX = w / Screen.width;
+            var scaleY = h / Screen.height;
+
+            _root.style.paddingTop    = (Screen.height - safe.yMax) * scaleY;
+            _root.style.paddingBottom = safe.y * scaleY;
+            _root.style.paddingLeft   = safe.x * scaleX;
+            _root.style.paddingRight  = (Screen.width - safe.xMax) * scaleX;
+
+            _lastSafeArea = safe;
+        }
+
         // ---- Typed-events accordion construction ----
 
         // Each accordion's Send button captures its EventSpec + input dictionary