feat(search): index PDF text, OCR scanned PDFs on import

Search now covers handwriting, the PDF text layer, AND scanned
(rasterized) PDFs.

- PdfTextIndexer runs at import: sums the embedded text layer across
  pages; if present it stores that as the document body, otherwise the
  PDF is rasterized and its rendered pages are OCR'd in the background.
  The result lands in the sidecar `pageText` field (distinct from
  `ocrText`, the handwriting OCR). Idempotent (skips a sidecar that
  already has pageText); degrades gracefully with no OCR engine.
- pdfrx_page_text_source abstracts text/render so it's testable.
- VaultSearchIndex now harvests title + typed text + handwriting OCR +
  PDF pageText, so search finds notes, typed PDFs and scanned PDFs.

analyze clean, 409 tests green.

lib/screens/home_screen.dart

@@ -1,3 +1,5 @@
+import 'dart:async';
+
 import 'package:file_picker/file_picker.dart';
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
@@ -8,6 +10,7 @@ import '../models/note.dart';
 import '../providers/document_provider.dart';
 import '../providers/note_provider.dart';
 import '../providers/ocr_provider.dart';
+import '../providers/search_provider.dart';
 import '../editor/canvas/pen_editor_screen.dart';
 import '../services/pptx_service.dart';
 import '../services/vault_service.dart';
@@ -250,6 +253,10 @@ class HomeScreen extends ConsumerWidget {
       final vaultPath = await vault.createNotebook(pickedPath);
       // Refresh the documents list so the new notebook shows on return.
       await ref.read(documentListProvider.notifier).loadDocuments();
+      // For a PDF, index its document body (embedded text layer, or background
+      // OCR of a rasterized/scanned PDF) into the sidecar so search covers it.
+      // Fire-and-forget: import returns and opens the editor immediately.
+      _indexPdfInBackground(ref, vaultPath);
       if (!context.mounted) return;
       await _openVaultFile(context, ref, vaultPath);
     } catch (e) {
@@ -257,6 +264,25 @@ class HomeScreen extends ConsumerWidget {
     }
   }
 
+  /// Kick off background document-body indexing for an in-vault PDF (no-op for
+  /// other types). Runs detached from the import await chain so the editor opens
+  /// immediately; on completion it bumps the search-index epoch so the newly
+  /// indexed text is searchable. Idempotency and graceful OCR degradation live in
+  /// [PdfTextIndexer]; failures here are swallowed (search just misses the body).
+  void _indexPdfInBackground(WidgetRef ref, String vaultPath) {
+    final ext = p.extension(vaultPath).replaceFirst('.', '').toLowerCase();
+    if (ext != 'pdf') return;
+    final indexer = ref.read(pdfTextIndexerProvider);
+    unawaited(() async {
+      final indexed = await indexer.indexPdf(vaultPath);
+      if (indexed != null && indexed.isNotEmpty) {
+        // Force the next search to re-scan the vault (picks up the new pageText).
+        final epoch = ref.read(searchIndexEpochProvider.notifier);
+        epoch.state = epoch.state + 1;
+      }
+    }());
+  }
+
   /// Route an in-vault [filePath] to the correct editor by extension:
   /// pdf → [PenEditorScreen]; pptx/ppt → [PenSlideScreen]; docx → convert to
   /// PDF (best-effort, LibreOffice) then open as PDF. Unsupported / failed