fix(ui): bind visible skills scrollbar

src/AcDream.App/UI/Layout/CharacterStatController.cs

@@ -621,8 +621,13 @@ public static class CharacterStatController
         if (spriteResolve is null)
             return null;
 
-        UiElement? source =
-            (contentPage is not null
+        // The mounted character sublayout contains duplicated stat-management
+        // branches with the same element ids. Bind the scrollbar adjacent to the
+        // active list first; a page-wide DFS can select an inactive duplicate that
+        // is never drawn while leaving the visible gutter unconfigured.
+        UiElement? source = statList?.Parent?.Children.FirstOrDefault(
+                static el => HasDatElementId(el, ListScrollbarId))
+            ?? (contentPage is not null
                 ? FindInSubtree(contentPage, static el => HasDatElementId(el, ListScrollbarId))
                 : null)
             ?? layout.FindElement(ListScrollbarId);
@@ -1674,7 +1679,17 @@ public static class CharacterStatController
         => DatElementId(element) == id;
 
     private static uint DatElementId(UiElement element)
-        => element switch
+    {
+        // DatWidgetFactory assigns the canonical id on every imported widget,
+        // including behavioral types such as UiScrollbar that do not expose a
+        // type-specific ElementId property. Prefer it so subtree role lookup is
+        // independent of the concrete widget class. The fallbacks keep the small
+        // hand-built controller fixtures working when they construct widgets
+        // directly instead of through the factory.
+        if (element.DatElementId != 0u)
+            return element.DatElementId;
+
+        return element switch
         {
             UiDatElement datElement => datElement.ElementId,
             UiButton button => button.ElementId,
@@ -1682,6 +1697,7 @@ public static class CharacterStatController
             UiText text => text.ElementId,
             _ => 0u,
         };
+    }
 
     private static UiElement? FindElementByDatId(ImportedLayout layout, UiElement? scope, uint id)
     {