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/stroke_predictor_test.dart

@@ -0,0 +1,28 @@
+import 'dart:ui';
+
+import 'package:flutter_test/flutter_test.dart';
+
+import 'package:badnote/editor/engine/stroke_predictor.dart';
+
+void main() {
+  test('StrokePredictor projects ahead when velocity is high', () {
+    final p = StrokePredictor(lookaheadMs: 16);
+    final t0 = DateTime.utc(2026, 1, 1, 0, 0, 0, 0);
+    expect(p.observe(const Offset(0, 0), 0.5, at: t0), isNull);
+    final tip = p.observe(
+      const Offset(10, 0),
+      0.5,
+      at: t0.add(const Duration(milliseconds: 8)),
+    );
+    // 10px / 8ms ≈ 1250 px/s → 16ms lookahead ≈ 20px ahead
+    expect(tip, isNotNull);
+    expect(tip!.offset.dx, greaterThan(10));
+  });
+
+  test('StrokePredictor resets cleanly', () {
+    final p = StrokePredictor();
+    p.observe(const Offset(0, 0), 0.4);
+    p.reset();
+    expect(p.observe(const Offset(1, 1), 0.4), isNull);
+  });
+}