feat: unified shell, diagnostics pack, native Office, sticky board

Make Surface remote debugging and classroom workflows viable: always-on
structured logs with one-click zip export, a single AppShell chrome,
OOXML PPTX/DOCX annotation without LibreOffice, and a first-class sticky
board. Also drop spike/legacy ink widgets and tighten pen feel
(predictor, PenInfoHistory, page-tile layer).

Co-authored-by: Cursor <cursoragent@cursor.com>

test/page_tile_layer_test.dart

@@ -0,0 +1,42 @@
+import 'dart:ui' as ui;
+
+import 'package:flutter_test/flutter_test.dart';
+
+import 'package:badnote/editor/pdf/page_tile_cache.dart';
+import 'package:badnote/editor/pdf/page_tile_layer.dart';
+
+void main() {
+  TestWidgetsFlutterBinding.ensureInitialized();
+
+  test('PageTileCache LRU evicts oldest', () async {
+    final cache = PageTileCache(maxTiles: 2);
+    final a = await _tinyImage();
+    final b = await _tinyImage();
+    final c = await _tinyImage();
+    cache.put(const TileKey('p1', 96), a);
+    cache.put(const TileKey('p2', 96), b);
+    expect(cache.length, 2);
+    cache.put(const TileKey('p3', 96), c);
+    expect(cache.length, 2);
+    expect(cache.get(const TileKey('p1', 96)), isNull);
+  });
+
+  test('PageTileLayer falls back to last good', () async {
+    final layer = PageTileLayer(cache: PageTileCache(maxTiles: 4));
+    final img = await _tinyImage();
+    layer.put(const TileKey('p1', 96), img);
+    expect(layer.resolve(const TileKey('p1', 192)), same(img));
+    // Don't call dispose() in unit test — cache dispose needs a frame.
+  });
+}
+
+Future<ui.Image> _tinyImage() async {
+  final recorder = ui.PictureRecorder();
+  final canvas = ui.Canvas(recorder);
+  canvas.drawRect(
+    const ui.Rect.fromLTWH(0, 0, 2, 2),
+    ui.Paint()..color = const ui.Color(0xFFFFFFFF),
+  );
+  final picture = recorder.endRecording();
+  return picture.toImage(2, 2);
+}