fix(ui): Campaign LA gate round 2 — character-select scales as one authored canvas

Third iteration on the screen, completing AD-98. The previous substitution
stretched only the root BACKGROUND while the child widgets stayed at their
authored 800x600 pixel positions - and the background painting carries
visual anchors (the World/Characters captions are art), so the user gate
showed captions overlapping the listbox and every widget misaligned
against the stretched art.

Retail model (established at 71bf24fb): fixed-canvas pre-world screens
render at authored 800x600 and the whole composed frame stretches once at
presentation; the blitter has no stretch mode. Our equivalent now does the
same one stage earlier:

- UiRoot.FixedCanvasSize: while the char-select screen is active, the
  retained tree lays out in its authored canvas and Draw scopes a uniform
  scale onto TextRenderer.CanvasScale; the mouse entry points apply the
  exact inverse so MouseX/MouseY and every hit test live in canvas space.
- TextRenderer.AppendQuad is the single emission chokepoint - sprites,
  rects, AND glyphs scale together, including retail-authentic non-uniform
  aspect distortion and stretched text. World-space HUD stays native (the
  scale resets outside UiRoot.Draw).
- CharacterManagementUiController stops resizing Root to the viewport;
  activate/deactivate/dispose set and clear the host canvas.
- UiDatElement returns to retail-pure copy-or-tile; the interim
  StretchOwnBackgroundToFill flag is deleted.
- AD-98 updated to describe the completed substitution.

Tests: canvas-scale quad math, inverse input mapping (window click lands
on the canvas-space widget), degenerate-size guards, controller keeps
authored extent + sets/clears the canvas. App suite 5085/6 skips; live-DAT
char-select probes 3/3.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

tests/AcDream.App.Tests/UI/UiRootFixedCanvasTests.cs

@@ -0,0 +1,121 @@
+using System.Numerics;
+using AcDream.App.UI;
+using AcDream.App.UI.Layout;
+using Xunit;
+
+namespace AcDream.App.Tests.UI;
+
+/// <summary>
+/// Campaign LA gate round 2 (register AD-98): retail renders fixed-canvas
+/// pre-world screens (char select, authored 800×600) at authored size and
+/// stretches the whole composed frame at presentation — its UI blitter has no
+/// stretch mode. acdream's equivalent is <see cref="UiRoot.FixedCanvasSize"/>:
+/// draw applies one uniform scale at the renderer's quad chokepoint, and the
+/// mouse entry points apply the exact inverse so hit-testing lives in canvas
+/// space. These tests pin the scale math and the inverse input mapping — the
+/// half that, if wrong, makes the user click on art and hit nothing.
+/// </summary>
+public class UiRootFixedCanvasTests
+{
+    [Fact]
+    public void CanvasScale_IsOne_WithoutFixedCanvas()
+    {
+        var root = new UiRoot { Width = 1920f, Height = 1080f };
+        Assert.Equal(Vector2.One, root.CanvasScale);
+    }
+
+    [Fact]
+    public void CanvasScale_IsWindowOverCanvas_WhenFixed()
+    {
+        var root = new UiRoot
+        {
+            Width = 1920f,
+            Height = 1080f,
+            FixedCanvasSize = new Vector2(800f, 600f),
+        };
+        Assert.Equal(new Vector2(2.4f, 1.8f), root.CanvasScale);
+    }
+
+    [Fact]
+    public void CanvasScale_IsOne_ForDegenerateCanvasOrWindow()
+    {
+        var zeroCanvas = new UiRoot
+        {
+            Width = 1920f,
+            Height = 1080f,
+            FixedCanvasSize = new Vector2(0f, 600f),
+        };
+        Assert.Equal(Vector2.One, zeroCanvas.CanvasScale);
+
+        var zeroWindow = new UiRoot
+        {
+            Width = 0f,
+            Height = 0f,
+            FixedCanvasSize = new Vector2(800f, 600f),
+        };
+        Assert.Equal(Vector2.One, zeroWindow.CanvasScale);
+    }
+
+    /// <summary>
+    /// The load-bearing inverse: a click at WINDOW coordinates must land on the
+    /// widget whose authored CANVAS rect the user visually clicked. The button
+    /// sits at canvas (300,400)+(120×40); at a 1920×1080 window over an 800×600
+    /// canvas it appears at window (720,720)-(1008,792). Clicking window
+    /// (860,750) — canvas (358,417) — must click it; clicking window (300,400)
+    /// — canvas (125,222), visually empty — must not.
+    /// </summary>
+    [Fact]
+    public void MouseInput_MapsWindowCoordsToCanvasSpace()
+    {
+        var root = new UiRoot
+        {
+            Width = 1920f,
+            Height = 1080f,
+            FixedCanvasSize = new Vector2(800f, 600f),
+        };
+        int clicks = 0;
+        var button = new UiButton(
+            new ElementInfo { Width = 120, Height = 40 },
+            _ => (0u, 0, 0))
+        {
+            Left = 300f,
+            Top = 400f,
+            Width = 120f,
+            Height = 40f,
+            OnClick = () => clicks++,
+        };
+        root.AddChild(button);
+
+        root.OnMouseDown(UiMouseButton.Left, 860, 750);
+        root.OnMouseUp(UiMouseButton.Left, 860, 750);
+        Assert.Equal(1, clicks);
+        Assert.Equal(358, root.MouseX);
+        Assert.Equal(417, root.MouseY);
+
+        root.OnMouseDown(UiMouseButton.Left, 300, 400);
+        root.OnMouseUp(UiMouseButton.Left, 300, 400);
+        Assert.Equal(1, clicks);
+    }
+
+    [Fact]
+    public void MouseInput_IsUntouched_WithoutFixedCanvas()
+    {
+        var root = new UiRoot { Width = 1920f, Height = 1080f };
+        int clicks = 0;
+        var button = new UiButton(
+            new ElementInfo { Width = 120, Height = 40 },
+            _ => (0u, 0, 0))
+        {
+            Left = 300f,
+            Top = 400f,
+            Width = 120f,
+            Height = 40f,
+            OnClick = () => clicks++,
+        };
+        root.AddChild(button);
+
+        root.OnMouseDown(UiMouseButton.Left, 360, 420);
+        root.OnMouseUp(UiMouseButton.Left, 360, 420);
+        Assert.Equal(1, clicks);
+    }
+}