fix(D.5.1): occupancy-gated slot numbers (empty=0x1000005e bg digit) + bottom-right rect probe

FIX 1: UIElement_UIItem::SetShortcutNum (decomp 229481) has a three-way source
branch: occupied+peace -> 0x10000042 (peace digit set), occupied+war -> 0x10000043
(war digit set), empty (ItemId==0) -> 0x1000005e (background digit, stance-independent).
acdream previously only had the peace/war pair and drew them regardless of occupancy.

Changes:
- GameWindow.cs: read property 0x1000005e into toolbarEmptyDigits (no fallback;
  null is safe). Logs entry count. Passes emptyDigits to Bind. Adds [D.5.1 probe]
  block logging screen pos + size of 7 bottom-right element ids via ScreenPosition.
- ToolbarController.cs: adds _emptyDigits field, emptyDigits ctor+Bind param (null
  default). RestampShortcutNumbers sets cell.EmptyDigits. Comments cite decomp 229481.
- UiItemSlot.cs: adds EmptyDigits property + ActiveDigitArray() internal testable seam
  (occupied -> peace/war by stance; empty -> EmptyDigits). OnDraw uses it. Comment
  updated with three-way source table.
- Tests: 5 new UiItemSlotTests (ActiveDigitArray occupancy), 2 new
  ToolbarControllerTests (emptyDigits injection + null-safe).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/AcDream.App/UI/UiItemSlot.cs

@@ -52,12 +52,20 @@ public sealed class UiItemSlot : UiElement
     public bool ShortcutPeace { get; private set; } = true;
 
     /// <summary>Peace digit DID array. Index i → digit (i+1) sprite RenderSurface id.
-    /// Injected by the controller after reading LayoutDesc 0x21000037.</summary>
+    /// Injected by the controller after reading LayoutDesc 0x21000037.
+    /// Retail ref: UIElement_UIItem::SetShortcutNum (decomp 229481) — occupied slot picks
+    /// property 0x10000042 (peace) or 0x10000043 (war) by stance.</summary>
     public uint[]? PeaceDigits { get; set; }
 
-    /// <summary>War digit DID array. Same layout as PeaceDigits.</summary>
+    /// <summary>War digit DID array. Same layout as PeaceDigits.
+    /// Retail ref: UIElement_UIItem::SetShortcutNum (decomp 229493) — war stance.</summary>
     public uint[]? WarDigits { get; set; }
 
+    /// <summary>Empty-slot digit DID array (property 0x1000005e, stance-independent).
+    /// Used when the slot is EMPTY (ItemId == 0). Retail ref: UIElement_UIItem::SetShortcutNum
+    /// (decomp 229481) — else branch when m_elem_Icon->m_state == 0x1000001c (empty).</summary>
+    public uint[]? EmptyDigits { get; set; }
+
     /// <summary>Set the slot's shortcut position and combat stance so the correct digit
     /// is drawn. Call with index 0..8 for the top row; pass peace=true for NonCombat.</summary>
     public void SetShortcutNum(int index, bool peace)
@@ -69,6 +77,20 @@ public sealed class UiItemSlot : UiElement
     /// <summary>Clear the shortcut number label (hides the digit).</summary>
     public void ClearShortcutNum() { ShortcutNum = -1; }
 
+    /// <summary>
+    /// Returns the digit DID array that OnDraw will use, following the retail occupancy
+    /// branch in UIElement_UIItem::SetShortcutNum (decomp 229481):
+    ///   occupied (ItemId != 0) → ShortcutPeace ? PeaceDigits : WarDigits (0x10000042/43)
+    ///   empty    (ItemId == 0) → EmptyDigits (0x1000005e, stance-independent)
+    /// Exposed as an internal method so unit tests can assert array selection without
+    /// needing a real render context.
+    /// </summary>
+    internal uint[]? ActiveDigitArray()
+    {
+        bool occupied = ItemId != 0;
+        return occupied ? (ShortcutPeace ? PeaceDigits : WarDigits) : EmptyDigits;
+    }
+
     // ── Events / draw ─────────────────────────────────────────────────────────
 
     /// <summary>Invoked by <see cref="OnEvent"/> when a left-button-down lands on
@@ -84,10 +106,8 @@ public sealed class UiItemSlot : UiElement
 
     protected override void OnDraw(UiRenderContext ctx)
     {
-        // Draw the icon (filled slot) or the empty-slot border. Both paths fall
-        // through to the digit draw below, so the slot label shows on all top-row
-        // slots regardless of whether they hold an item (retail screenshot confirms
-        // numbers on empty slots).
+        // Draw the icon (filled slot) or the empty-slot border. Both paths fall through
+        // to the digit draw below; the slot label always shows on top-row slots.
         if (ItemId != 0 && IconTexture != 0)
         {
             ctx.DrawSprite(IconTexture, 0f, 0f, Width, Height, 0f, 0f, 1f, 1f, Vector4.One);
@@ -100,11 +120,14 @@ public sealed class UiItemSlot : UiElement
         }
 
         // Digit overlay: UIElement_UIItem::SetShortcutNum (acclient_2013_pseudo_c.txt:229465).
-        // Each digit image is corner-baked (glyph in top-left, rest alpha=0) so we
-        // draw it full-cell size and the transparent region is invisible. DrawMode=Alphablend.
+        // Occupancy branch (decomp 229481):
+        //   occupied (ItemId != 0) → peace/war digit set 0x10000042/43, split by stance
+        //   empty    (ItemId == 0) → background digit set 0x1000005e, stance-independent
+        // Each digit image is corner-baked (glyph in top-left, rest alpha=0); drawn
+        // full-cell Alphablend so the transparent region is invisible.
         if (ShortcutNum >= 0 && SpriteResolve is not null)
         {
-            var arr = ShortcutPeace ? PeaceDigits : WarDigits;
+            var arr = ActiveDigitArray();
             if (arr is not null && ShortcutNum < arr.Length)
             {
                 uint did = arr[ShortcutNum];