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/storage/badnote_sidecar.dart

@@ -224,6 +224,7 @@ class BadnoteSidecar {
     Map<int, String>? legacyAnnotations,
     this.ocrText,
     this.legacyId,
+    this.background,
   })  : strokes = strokes ?? <int, List<EditorStroke>>{},
         highlights = highlights ?? <int, List<SidecarHighlight>>{},
         bookmarks = bookmarks ?? <Bookmark>[],
@@ -278,6 +279,12 @@ class BadnoteSidecar {
   /// its folder name collided). Null for all freshly authored sidecars.
   final String? legacyId;
 
+  /// The page-background template for a standalone notebook, stored as the
+  /// [NoteBackground] enum `name` (e.g. `dots`, `cornell`). Kept as a raw String
+  /// here so the storage model stays UI-decoupled; the editor decodes it via
+  /// `noteBackgroundFromName` (missing/unknown → blank, back-compat).
+  final String? background;
+
   Map<String, dynamic> toJson() => {
         'badnoteSidecarVersion': version,
         if (sourceFile != null) 'sourceFile': sourceFile,
@@ -306,6 +313,7 @@ class BadnoteSidecar {
           },
         if (ocrText != null && ocrText!.isNotEmpty) 'ocrText': ocrText,
         if (legacyId != null) 'legacyId': legacyId,
+        if (background != null) 'background': background,
       };
 
   factory BadnoteSidecar.fromJson(Map<String, dynamic> json) {
@@ -361,6 +369,7 @@ class BadnoteSidecar {
       }(),
       ocrText: json['ocrText'] as String?,
       legacyId: json['legacyId'] as String?,
+      background: json['background'] as String?,
     );
   }
 }