feat(note): page background templates (rnote-style)

A blank note can show a page-background template painted behind the
ink, picked from the toolbar and persisted per notebook.

- NoteBackground: blank / dots / ruled / grid / cornell, drawn in
  page space (scales with zoom), subtle grey. Cornell = left margin +
  bottom summary rule over a ruled body.
- Stored as the enum name in the notebook sidecar (back-compat:
  missing/unknown -> blank), saved/loaded via SidecarRepository so it
  restores on reopen.
- Picker added to the note tool palette.

PDF backgrounds skipped (PDFs have their own page content). analyze
clean, 386 tests green.

lib/editor/canvas/pen_note_screen.dart

@@ -24,6 +24,7 @@ import '../layout/viewport_fit.dart';
 import '../notebook/ink_stroke_adapter.dart';
 import '../ui/pen_settings_page.dart';
 import 'editor_tool.dart';
+import 'note_background.dart';
 import 'pen_canvas.dart';
 import 'pen_palette_widgets.dart';
 import 'pen_stroke.dart';
@@ -83,6 +84,10 @@ class _PenNoteScreenState extends ConsumerState<PenNoteScreen> {
   /// The active drawing color (the active brush's remembered color).
   Color get _color => _brushColors[_activeColorBrush] ?? Colors.black;
 
+  /// The page-background template painted behind the ink (rnote-style). Default
+  /// blank; persisted per-notebook in the sidecar.
+  NoteBackground _background = NoteBackground.blank;
+
   bool _allowFingerDrawing = false;
   bool _dirty = false;
   bool _needsCenter = true;
@@ -151,6 +156,7 @@ class _PenNoteScreenState extends ConsumerState<PenNoteScreen> {
       if (title != null && title.isNotEmpty) {
         _titleController.text = title;
       }
+      _background = noteBackgroundFromName(repo.loadedBackground);
     });
   }
 
@@ -288,6 +294,7 @@ class _PenNoteScreenState extends ConsumerState<PenNoteScreen> {
       for (final s in _strokes) EditorStroke.fromPenStroke(s),
     ];
     repo.scheduleTitleSave(title);
+    repo.scheduleBackgroundSave(_background.name);
     repo.scheduleStrokeSave(_notePageIndex, editorStrokes);
     await repo.flush();
 
@@ -475,8 +482,10 @@ class _PenNoteScreenState extends ConsumerState<PenNoteScreen> {
           allowFingerDrawing: _allowFingerDrawing,
           onStrokeComplete: _commitStroke,
           onEraseStroke: _eraseStroke,
-          // A white sheet with a soft shadow — the note "paper".
-          pageWidget: Container(
+          // A white sheet with a soft shadow — the note "paper" — overlaid with
+          // the selected background template, painted in page-pixel space (so it
+          // scales with zoom) and BEHIND the ink layers.
+          pageWidget: DecoratedBox(
             decoration: BoxDecoration(
               color: Colors.white,
               boxShadow: [
@@ -487,6 +496,10 @@ class _PenNoteScreenState extends ConsumerState<PenNoteScreen> {
                 ),
               ],
             ),
+            child: CustomPaint(
+              painter: NoteBackgroundPainter(_background),
+              size: Size.infinite,
+            ),
           ),
         );
       },
@@ -570,6 +583,55 @@ class _PenNoteScreenState extends ConsumerState<PenNoteScreen> {
             PaletteDivider(cs: cs),
             for (final c in _palette) _colorDot(c, cs),
             PaletteDivider(cs: cs),
+            // Page-background template picker (rnote-style: blank / dots / ruled
+            // / grid / cornell). Persists per-notebook in the sidecar.
+            PopupMenuButton<NoteBackground>(
+              tooltip: 'Page background',
+              initialValue: _background,
+              onSelected: (b) {
+                setState(() {
+                  _background = b;
+                  _dirty = true;
+                });
+              },
+              itemBuilder: (context) => [
+                for (final b in NoteBackground.values)
+                  PopupMenuItem<NoteBackground>(
+                    value: b,
+                    child: Row(
+                      mainAxisSize: MainAxisSize.min,
+                      children: [
+                        Icon(noteBackgroundIcon(b), size: 20),
+                        const SizedBox(width: 10),
+                        Text(noteBackgroundLabel(b)),
+                        if (b == _background) ...[
+                          const SizedBox(width: 8),
+                          Icon(Icons.check, size: 18, color: cs.primary),
+                        ],
+                      ],
+                    ),
+                  ),
+              ],
+              child: Padding(
+                padding: const EdgeInsets.symmetric(horizontal: 6, vertical: 8),
+                child: Row(
+                  mainAxisSize: MainAxisSize.min,
+                  children: [
+                    Icon(
+                      noteBackgroundIcon(_background),
+                      size: 22,
+                      color: cs.onSurfaceVariant,
+                    ),
+                    Icon(
+                      Icons.arrow_drop_down,
+                      size: 18,
+                      color: cs.onSurfaceVariant,
+                    ),
+                  ],
+                ),
+              ),
+            ),
+            PaletteDivider(cs: cs),
             ToolButton(
               icon: _allowFingerDrawing ? Icons.touch_app : Icons.do_not_touch,
               selected: _allowFingerDrawing,