fix(docs): correct real-time updates and search implementation status

Both features ARE already implemented:

Real-time Updates (WebSocket):
- Connection manager with broadcast loop
- Progress updates broadcast to all connected clients
- Conflict notifications
- Sync completion events
- Endpoint: /ws/sync

Advanced Search:
- Partial matching search (title, author, series)
- Fuzzy search with word_similarity > 0.3
- Fallback from exact to fuzzy matching
- Endpoint: GET /api/media-items/search?q=query

These were incorrectly listed as limitations. The actual remaining
limitations are:
- Rule testing preview
- Bulk operations
- Collection-specific search integration
- Real-time collection view updates (WebSocket exists but not used in collections UI)

PHASE_9_COMPLETION.md

@@ -241,11 +241,12 @@
 ### Current Limitations
 1. **Rule Testing**: Collection rules preview not yet implemented
 2. **Bulk Operations**: Batch book operations not yet available
-3. **Search**: Full-text search not integrated with collections
-4. **Real-time Updates**: WebSocket integration for live updates pending
+3. **Collection Search**: Search not integrated into collections UI (search exists globally)
+4. **Real-time Collection Updates**: WebSocket exists but not yet integrated into collection views
 
 ### ✅ Already Implemented (Previous Phases)
 The following features are **COMPLETE** and were implemented in earlier phases:
+
 1. **OPDS Integration**: ✅ Complete (Phase 5) - `internal/handlers/opds.go`
    - OPDS catalog feeds per device
    - Format conversion (EPUB → KEPUB)
@@ -264,6 +265,21 @@ The following features are **COMPLETE** and were implemented in earlier phases:
    - Winner selection (Kobo, KOReader, Web, Manual)
    - WebSocket notifications
 
+4. **Real-time Updates**: ✅ Complete - `internal/sync/websocket.go`, `internal/handlers/websocket.go`
+   - WebSocket connection manager
+   - Progress update broadcasts
+   - Annotation update broadcasts
+   - Conflict detection notifications
+   - Sync completion events
+   - Route: `/ws/sync`
+
+5. **Advanced Search**: ✅ Complete - `internal/handlers/ebook.go`
+   - Partial matching search (title, author, series)
+   - Fuzzy search with word_similarity (threshold > 0.3)
+   - ILIKE pattern matching for fast results
+   - Fuzzy fallback when no exact matches
+   - Route: `GET /api/media-items/search?q=query`
+
 ### Future Enhancements (Phase 10+)
 1. **Analytics**: Reading statistics and insights dashboard
 2. **Export**: Collection export to OPML/JSON formats