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/persistence/sidecar_repository.dart

@@ -145,6 +145,10 @@ class SidecarRepository {
   /// The standalone-notebook title loaded from the sidecar, or null.
   String? get loadedTitle => _sidecar.title;
 
+  /// The page-background template name loaded from the sidecar, or null
+  /// (missing → blank, decoded by the editor).
+  String? get loadedBackground => _sidecar.background;
+
   // ── Mutations (synchronous in-memory update + debounced atomic write) ──────
 
   /// Replace the standalone-notebook title and schedule a save. No-op if the
@@ -154,6 +158,13 @@ class SidecarRepository {
     _replace(title: title);
   }
 
+  /// Replace the page-background template (a [NoteBackground] enum name) and
+  /// schedule a save. No-op if unchanged.
+  void scheduleBackgroundSave(String background) {
+    if (_sidecar.background == background) return;
+    _replace(background: background);
+  }
+
   /// Replace the handwriting-OCR search text and schedule a save (Phase 6
   /// search index). No-op if unchanged.
   void scheduleOcrTextSave(String? ocrText) {
@@ -266,6 +277,7 @@ class SidecarRepository {
     List<SidecarScratchLink>? scratchLinks,
     String? ocrText,
     bool clearOcrText = false,
+    String? background,
   }) {
     if (_disposed) return;
     _sidecar = BadnoteSidecar(
@@ -282,6 +294,7 @@ class SidecarRepository {
       bookmarks: _sidecar.bookmarks,
       scratchLinks: scratchLinks ?? _sidecar.scratchLinks,
       ocrText: clearOcrText ? null : (ocrText ?? _sidecar.ocrText),
+      background: background ?? _sidecar.background,
     );
     _timer?.cancel();
     _timer = Timer(_debounce, () {