fix(desktop): match DMG background resolution to Finder layout

scripts/desktop-tauri-build.test.mjs

@@ -68,6 +68,31 @@ test('Desktop DMG uses the branded installer layout', () => {
     appPosition: { x: 180, y: 170 },
     applicationFolderPosition: { x: 480, y: 170 },
   });
+
+  // Finder uses the PNG's physical size, not just its pixel dimensions.
+  // A 660x400 image tagged at 96 DPI renders at 495x300 points and leaves gaps.
+  const dmg = config.bundle.macOS.dmg;
+  const background = readFileSync(join(ROOT, 'src', 'apps', 'desktop', dmg.background));
+  assert.deepEqual(background.subarray(0, 8), Buffer.from('89504e470d0a1a0a', 'hex'));
+  let pixels;
+  let density;
+  for (let offset = 8; offset < background.length; ) {
+    const length = background.readUInt32BE(offset);
+    const type = background.toString('ascii', offset + 4, offset + 8);
+    if (type === 'IHDR') {
+      pixels = [background.readUInt32BE(offset + 8), background.readUInt32BE(offset + 12)];
+    } else if (type === 'pHYs') {
+      assert.equal(background[offset + 16], 1, 'background density must be in pixels per metre');
+      density = [background.readUInt32BE(offset + 8), background.readUInt32BE(offset + 12)];
+    }
+    offset += length + 12;
+  }
+  assert.ok(pixels && density, 'DMG background must declare pixel dimensions and physical density');
+  for (const [axis, points] of [dmg.windowSize.width, dmg.windowSize.height].entries()) {
+    const imagePoints = pixels[axis] * 72 / (density[axis] * 0.0254);
+    // PNG stores integer pixels/metre, so 72 DPI rounds to 2835 pixels/metre.
+    assert.ok(Math.abs(imagePoints - points) < 0.1, `background axis ${axis} must match Finder points`);
+  }
 });
 
 test('Desktop builds prepare and bundle the OpenCode extension Host', () => {